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Graph Signal Active Contours

Olivier Lezoray

Auto-TLDR; Adaptation of Active Contour Without Edges for Graph Signal Processing

Abstract Slides

With the advent of data living on vertices of graphs, there is much interest in processing the so-called graph signals for partitioning tasks. As active contours have had much impact in the image processing community, their formulation on graphs is of importance to the field of graph signal processing. This paper proposes an adaptation on graphs of a model that combines the Geodesic Active Contour and the Active Contour Without Edges models. In addition, specific terms depending on graphs are introduced in the formulation. This adaptation is solved using a level set formulation with a gradient descent that can be expressed as a morphological front evolution process. Experimental results on different kinds of graphs signals show the benefit of the approach.

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A New Geodesic-Based Feature for Characterization of 3D Shapes: Application to Soft Tissue Organ Temporal Deformations

Karim Makki, Amine Bohi, Augustin Ogier, Marc-Emmanuel Bellemare

Auto-TLDR; Spatio-Temporal Feature Descriptors for 3D Shape Characterization from Point Clouds

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Spatio-temporal feature descriptors are of great importance for characterizing the local changes of 3D deformable shapes. In this study, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations. As an example, we characterize the behavior of the bladder during forced respiratory motion with a reduced number of 3D surface points: first, a set of equidistant points representing the vertices of quadrilateral mesh for the organ surface are tracked throughout a long dynamic MRI sequence using a large deformation diffeomorphic metric mapping (LDDMM) framework. Second, a novel 3D shape descriptor invariant to translation, scale and rotation is proposed for characterizing the temporal organ deformations by employing an Eulerian Partial Differential Equations (PDEs) methodology. We demonstrate the robustness of our feature on both synthetic 3D shapes and realistic dynamic Magnetic Resonance Imaging (MRI) data sequences portraying the bladder deformation during a forced breathing exercise. Promising results are obtained, showing that the proposed feature may be useful for several computer vision applications such as medical imaging, aerodynamics and robotics.

Facetwise Mesh Refinement for Multi-View Stereo

Andrea Romanoni, Matteo Matteucci

Auto-TLDR; Facetwise Refinement of Multi-View Stereo using Delaunay Triangulations

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Mesh refinement is a fundamental step for accurate Multi-View Stereo. It modifies the geometry of an initial manifold mesh to minimize the photometric error induced in a set of camera pairs. This initial mesh is usually the output of volumetric 3D reconstruction based on min-cut over Delaunay Triangulations. Such methods produce a significant amount of non-manifold vertices, therefore they require a vertex split step to explicitly repair them. In this paper we extend this method to preemptively fix the non-manifold vertices by reasoning directly on the Delaunay Triangulation and avoid most vertex splits. The main contribution of this paper addresses the problem of choosing the camera pairs adopted by the refinement process. We treat the problem as a mesh labeling process, where each label corresponds to a camera pair. Differently from the state-of-the-art methods, which use each camera pair to refine all the visible parts of the mesh, we choose, for each facet, the best pair that enforces both the overall visibility and coverage. The refinement step is applied for each facet using only the camera pair selected. This facetwise refinement helps the process to be applied in the most evenly way possible.

Local Binary Quaternion Rotation Pattern for Colour Texture Retrieval

Hela Jebali, Noel Richard, Mohamed Naouai

Auto-TLDR; Local Binary Quaternion Rotation Pattern for Color Texture Classification

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Color is very important feature for image representation, it assumes very essential in the human visual recognition process. Most existing approaches usually extract features from the three color channels separately (Marginal way). Although, it exists few vector expressions of texture features. Aware of the high interaction that exists between different channels in the color image, this work introduces a compact texture descriptor, named Local Binary Quaternion Rotation Pattern (LBQRP). In this LBQRP purpose, the quaternion representation is used to represent color texture. The distance between two color can be expressed as the angle of rotation between two unit quaternions using the geodesic distance. After a LBQRP coding, local histograms are extracted and used as features. Experiments on three challenging color datasets: Vistex, Outex-TC13 and USPtex are carried out to evaluate the LBQRP performance in texture classification. Results show the high efficiency of the proposed approach facing to several stat-of-art methods.

On Morphological Hierarchies for Image Sequences

Caglayan Tuna, Alain Giros, François Merciol, Sébastien Lefèvre

Auto-TLDR; Comparison of Hierarchies for Image Sequences

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Morphological hierarchies form a popular framework aiming at emphasizing the multiscale structure of digital image by performing an unsupervised spatial partitioning of the data. These hierarchies have been recently extended to cope with image sequences, and different strategies have been proposed to allow their construction from spatio-temporal data. In this paper, we compare these hierarchical representation strategies for image sequences according to their structural properties. We introduce a projection method to make these representations comparable. Furthermore, we extend one of these recent strategies in order to obtain more efficient hierarchical representations for image sequences. Experiments were conducted on both synthetic and real datasets, the latter being made of satellite image time series. We show that building one hierarchy by using spatial and temporal information together is more efficient comparing to other existing strategies.

Learning to Segment Clustered Amoeboid Cells from Brightfield Microscopy Via Multi-Task Learning with Adaptive Weight Selection

Rituparna Sarkar, Suvadip Mukherjee, Elisabeth Labruyere, Jean-Christophe Olivo-Marin

Auto-TLDR; Supervised Cell Segmentation from Microscopy Images using Multi-task Learning in a Multi-Task Learning Paradigm

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Detecting and segmenting individual cells from microscopy images is critical to various life science applications. Traditional cell segmentation tools are often ill-suited for applications in brightfield microscopy due to poor contrast and intensity heterogeneity, and only a small subset are applicable to segment cells in a cluster. In this regard, we introduce a novel supervised technique for cell segmentation in a multi-task learning paradigm. A combination of a multi-task loss, based on the region and cell boundary detection, is employed for an improved prediction efficiency of the network. The learning problem is posed in a novel min-max framework which enables adaptive estimation of the hyper-parameters in an automatic fashion. The region and cell boundary predictions are combined via morphological operations and active contour model to segment individual cells. The proposed methodology is particularly suited to segment touching cells from brightfield microscopy images without manual interventions. Quantitatively, we observe an overall Dice score of 0.93 on the validation set, which is an improvement of over 15.9% on a recent unsupervised method, and outperforms the popular supervised U-net algorithm by at least 5.8% on average.

Classification and Feature Selection Using a Primal-Dual Method and Projections on Structured Constraints

Michel Barlaud, Antonin Chambolle, Jean_Baptiste Caillau

Auto-TLDR; A Constrained Primal-dual Method for Structured Feature Selection on High Dimensional Data

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This paper deals with feature selection using supervised classification on high dimensional datasets. A classical approach is to project data on a low dimensional space and classify by minimizing an appropriate quadratic cost. Our first contribution is to introduce a matrix of centers in the definition of this cost. Moreover, as quadratic costs are not robust to outliers, we propose to use an $\ell_1$ cost instead (or Huber loss to mitigate overfitting issues). While control on sparsity is commonly obtained by adding an $\ell_1$ constraint on the vectorized matrix of weights used for projecting the data, our second contribution is to enforce structured sparsity. To this end we propose constraints that take into account the matrix structure of the data, based either on the nuclear norm, on the $\ell_{2,1}$ norm, or on the $\ell_{1,2}$ norm for which we provide a new projection algorithm. We optimize simultaneously the projection matrix and the matrix of centers thanks to a new tailored constrained primal-dual method. The primal-dual framework is general enough to encompass the various robust losses and structured constraints we use, and allows a convergence analysis. We demonstrate the effectiveness of the approach on three biological datasets. Our primal-dual method with robust losses, adaptive centers and structured constraints does significantly better than classical methods, both in terms of accuracy and computational time.

Graph Approximations to Geodesics on Metric Graphs

Robin Vandaele, Yvan Saeys, Tijl De Bie

Auto-TLDR; Topological Pattern Recognition of Metric Graphs Using Proximity Graphs

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In machine learning, high-dimensional point clouds are often assumed to be sampled from a topological space of which the intrinsic dimension is significantly lower than the representation dimension. Proximity graphs, such as the Rips graph or kNN graph, are often used as an intermediate representation to learn or visualize topological and geometrical properties of this space. The key idea behind this approach is that distances on the graph preserve the geodesic distances on the unknown space well, and as such, can be used to infer local and global geometric patterns of this space. Prior results provide us with conditions under which these distances are well-preserved for geodesically convex, smooth, compact manifolds. Yet, proximity graphs are ideal representations for a much broader class of spaces, such as metric graphs, i.e., graphs embedded in the Euclidean space. It turns out—as proven in this paper—that these existing conditions cannot be straightforwardly adapted to these spaces. In this work, we provide novel, flexible, and insightful characteristics and results for topological pattern recognition of metric graphs to bridge this gap.

Directional Graph Networks with Hard Weight Assignments

Miguel Dominguez, Raymond Ptucha

Auto-TLDR; Hard Directional Graph Networks for Point Cloud Analysis

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Point cloud analysis is an important field for 3D scene understanding. It has applications in self driving cars and robotics (via LIDAR sensors), 3D graphics, and computer-aided design. Neural networks have recently achieved strong results on point cloud analysis problems such as classification and segmentation. Each point cloud network has the challenge of defining a convolution that can learn useful features on unstructured points. Some recent point cloud convolutions create separate weight matrices for separate directions like a CNN, but apply every weight matrix to every neighbor with soft assignments. This increases computational complexity and makes relatively small neighborhood aggregations expensive to compute. We propose Hard Directional Graph Networks (HDGN), a point cloud model that both learns directional weight matrices and assigns a single matrix to each neighbor, achieving directional convolutions at lower computational cost. HDGN's directional modeling achieves state-of-the-art results on multiple point cloud vision benchmarks.

Generalized Shortest Path-Based Superpixels for Accurate Segmentation of Spherical Images

Rémi Giraud, Rodrigo Borba Pinheiro, Yannick Berthoumieu

Auto-TLDR; SPS: Spherical Shortest Path-based Superpixels

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Most of existing superpixel methods are designed to segment standard planar images as pre-processing for computer vision pipelines. Nevertheless, the increasing number of applications based on wide angle capture devices, mainly generating 360° spherical images, have enforced the need for dedicated superpixel approaches. In this paper, we introduce a new superpixel method for spherical images called SphSPS (for Spherical Shortest Path-based Superpixels). Our approach respects the spherical geometry and generalizes the notion of shortest path between a pixel and a superpixel center on the 3D spherical acquisition space. We show that the feature information on such path can be efficiently integrated into our clustering framework and jointly improves the respect of object contours and the shape regularity. To relevantly evaluate this last aspect in the spherical space, we also generalize a planar global regularity metric. Finally, the proposed SphSPS method obtains significantly better performances than both planar and spherical recent superpixel approaches on the reference 360 o spherical panorama segmentation dataset.

Offset Curves Loss for Imbalanced Problem in Medical Segmentation

Ngan Le, Duc Toan Bui, Khoa Luu, Marios Savvides

Auto-TLDR; Offset Curves Loss for Medical Image Segmentation

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Medical image segmentation has played an important role in medical analysis and widely developed for many clinical applications. Deep learning-based approaches have achieved high performance in semantic segmentation but they are limited to pixel-wise setting and imbalanced classes data problem. In this paper, we tackle those limitations by developing a new deep learning-based model which takes into account both higher feature level i.e. region inside contour, intermediate feature level i.e. offset curves around the contour and lower feature level i.e. contour. Our proposed Offset Curves (OsC) loss consists of three main fitting terms. The first fitting term focuses on pixel-wise level segmentation whereas the second fitting term acts as attention model which pays attention to the area around the boundaries (offset curves). The third terms plays a role as regularization term which takes the length of boundaries into account. We evaluate our proposed OsC loss on both 2D network and 3D network. Two common medical datasets, i.e. retina DRIVE and brain tumor BRATS 2018 datasets are used to benchmark our proposed loss performance. The experiments have showed that our proposed OsC loss function outperforms other mainstream loss functions such as Cross-Entropy, Dice, Focal on the most common segmentation networks Unet, FCN.

GraphBGS: Background Subtraction Via Recovery of Graph Signals

Jhony Heriberto Giraldo Zuluaga, Thierry Bouwmans

Auto-TLDR; Graph BackGround Subtraction using Graph Signals

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Background subtraction is a fundamental pre-processing task in computer vision. This task becomes challenging in real scenarios due to variations in the background for both static and moving camera sequences. Several deep learning methods for background subtraction have been proposed in the literature with competitive performances. However, these models show performance degradation when tested on unseen videos; and they require huge amount of data to avoid overfitting. Recently, graph-based algorithms have been successful approaching unsupervised and semi-supervised learning problems. Furthermore, the theory of graph signal processing and semi-supervised learning have been combined leading to new insights in the field of machine learning. In this paper, concepts of recovery of graph signals are introduced in the problem of background subtraction. We propose a new algorithm called Graph BackGround Subtraction (GraphBGS), which is composed of: instance segmentation, background initialization, graph construction, graph sampling, and a semi-supervised algorithm inspired from the theory of recovery of graph signals. Our algorithm has the advantage of requiring less data than deep learning methods while having competitive results on both: static and moving camera videos. GraphBGS outperforms unsupervised and supervised methods in several challenging conditions on the publicly available Change Detection (CDNet2014), and UCSD background subtraction databases.

Graph Discovery for Visual Test Generation

Neil Hallonquist, Laurent Younes, Donald Geman

Auto-TLDR; Visual Question Answering over Graphs: A Probabilistic Framework for VQA

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We consider the problem of uncovering an unknown attributed graph, where both its edges and vertices are hidden from view, through a sequence of binary questions about it. In order to select questions efficiently, we define a probability distribution over graphs, with randomness not just over edges, but over vertices as well. We then sequentially select questions so as to: (1) minimize the expected entropy of the random graph, given the answers to the previous questions in the sequence; and (2) to instantiate the vertices that compose the graph. We propose some basic question spaces, from which to select questions, that vary in their capacity. We apply this framework to the problem of test generation in Visual Question Answering (VQA), where semantic questions are used to evaluate vision systems over rich image representations. To do this, we use a restricted question vocabulary, resulting in image representations that take the form of scene graphs; by defining a distribution over them, a consistent set of probabilities is associated with the questions, and used in their selection.

Approach for Document Detection by Contours and Contrasts

Daniil Tropin, Sergey Ilyuhin, Dmitry Nikolaev, Vladimir V. Arlazarov

Auto-TLDR; A countor-based method for arbitrary document detection on a mobile device

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This paper considers the task of arbitrary document detection performed on a mobile device. The classical contour-based approach often mishandles cases with occlusion, complex background, or blur. Region-based approach, which relies on the contrast between object and background, does not have limitations, however its known implementations are highly resource-consuming. We propose a modification of a countor-based method, in which the competing hypotheses of the contour location are ranked according to the contrast between the areas inside and outside the border. In the performed experiments such modification leads to the 40% decrease of alternatives ordering errors and 10% decrease of the overall number of detection errors. We updated state-of-the-art performance on the open MIDV-500 dataset and demonstrated competitive results with the state-of-the-art on the SmartDoc dataset.

3D Semantic Labeling of Photogrammetry Meshes Based on Active Learning

Mengqi Rong, Shuhan Shen, Zhanyi Hu

Auto-TLDR; 3D Semantic Expression of Urban Scenes Based on Active Learning

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As different urban scenes are similar but still not completely consistent, coupled with the complexity of labeling directly in 3D, high-level understanding of 3D scenes has always been a tricky problem. In this paper, we propose a procedural approach for 3D semantic expression of urban scenes based on active learning. We first start with a small labeled image set to fine-tune a semantic segmentation network and then project its probability map onto a 3D mesh model for fusion, finally outputs a 3D semantic mesh model in which each facet has a semantic label and a heat model showing each facet’s confidence. Our key observation is that our algorithm is iterative, in each iteration, we use the output semantic model as a supervision to select several valuable images for annotation to co-participate in the fine-tuning for overall improvement. In this way, we reduce the workload of labeling but not the quality of 3D semantic model. Using urban areas from two different cities, we show the potential of our method and demonstrate its effectiveness.

Learning Sign-Constrained Support Vector Machines

Kenya Tajima, Kouhei Tsuchida, Esmeraldo Ronnie Rey Zara, Naoya Ohta, Tsuyoshi Kato

Auto-TLDR; Constrained Sign Constraints for Learning Linear Support Vector Machine

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Domain knowledge is useful to improve the generalization performance of learning machines. Sign constraints are a handy representation to combine domain knowledge with learning machine. In this paper, we consider constraining the signs of the weight coefficients in learning the linear support vector machine, and develop two optimization algorithms for minimizing the empirical risk under the sign constraints. One of the two algorithms is based on the projected gradient method, in which each iteration of the projected gradient method takes O(nd) computational cost and the sublinear convergence of the objective error is guaranteed. The second algorithm is based on the Frank-Wolfe method that also converges sublinearly and possesses a clear termination criterion. We show that each iteration of the Frank-Wolfe also requires O(nd) cost. Furthermore, we derive the explicit expression for the minimal iteration number to ensure an epsilon-accurate solution by analyzing the curvature of the objective function. Finally, we empirically demonstrate that the sign constraints are a promising technique when similarities to the training examples compose the feature vector.

Fast Blending of Planar Shapes Based on Invariant Invertible and Stable Descriptors

Emna Ghorbel, Faouzi Ghorbel, Ines Sakly, Slim Mhiri

Auto-TLDR; Fined-Fourier-based Invariant Descriptor for Planar Shape Blending

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In this paper, a novel method for blending planar shapes is introduced. This approach is based on the Fined-Fourier-based Invariant Descriptor (Fined-FID) that is invertible, invariant under Euclidean transformations and stable. Our approach extracts the Fined-FID from the two shapes of interest (the source and the target ones). Then, the extracted descriptors are averaged enabling the calculation of intermediate descriptors. Finally, thanks to the inversion criterion, the intermediate shapes are easily recovered by applying the inverse analytical expression to these intermediate descriptors. Compared to previous works, the Fined-FID-based morphing avoid the usual registration step, generates naturally closed intermediate contours and ensure invariance under Euclidean transformations and invariance to the starting point, while being computationally efficient (almost-linear complexity). The performed experiments show the performance of the proposed blending approach with respect to curvature-based methods.

Incorporating a Graph-Matching Algorithm into a Muscle Mechanics Model

Jose Luis Santacruz Muñoz, Francesc Serratosa

Auto-TLDR; Recomputing the Mesh Grid for Differential Models of the Muscle Mechanics

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Differential models for the simulation of the muscle mechanics are based on iteratively updating a mesh grid and deducing its new state through a finite element model. Models usually assume that the mesh grid is almost regular, and this makes a degradation of the simulation accuracy in long simulation sequences, since the mesh tends to be less regular when the number of iterations increases. We present a model that has the aim of reducing this accuracy degradation. It is based on recomputing the mesh grid returned by the model in each iteration through the concept of graph matching. The new model is currently in use to analyse the dynamics of the human heart when some pressure is applied to it. The final goal of the project (which is not shown in this paper) is to deduce the optimal position and strength pressure applied to the heart that increases the chance of reviving it with the minimum tissue damage. Experimental validation shows our model returns a higher accuracy of the muscle position through some iterations than classical differential models with an insignificant increase of runtime. Thus, it is worth recomputing the mesh grid since the simulation accuracy drastically increases at the expense of a low runtime increase.

Generalized Conics: Properties and Applications

Aysylu Gabdulkhakova, Walter Kropatsch

Auto-TLDR; A Generalized Conic Representation for Distance Fields

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In this paper the properties of the generalized conics are used to create a unified framework for generating various types of the distance fields. The main concept behind this work is a metric that measures the distance from a point to a line segment according to the definition of the ellipse. The proposed representation provides a possibility to efficiently compute the proximity, arithmetic mean of the distances and a space tessellation with regard to the given set of polygonal objects, line segments and points. In addition, the weights can be introduced for objects, their parts and combinations. This fact leads to a hierarchical representation that can be efficiently obtained using the pixel-wise operations. The practical value of the proposed ideas is demonstrated on example of applications like skeletonization, smoothing, optimal location finding and clustering.

Hcore-Init: Neural Network Initialization Based on Graph Degeneracy

Stratis Limnios, George Dasoulas, Dimitrios Thilikos, Michalis Vazirgiannis

Auto-TLDR; K-hypercore: Graph Mining for Deep Neural Networks

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Neural networks are the pinnacle of Artificial Intelligence, as in recent years we witnessed many novel architectures, learning and optimization techniques for deep learning. Capitalizing on the fact that neural networks inherently constitute multipartite graphs among neuron layers, we aim to analyze directly their structure to extract meaningful information that can improve the learning process. To our knowledge graph mining techniques for enhancing learning in neural networks have not been thoroughly investigated. In this paper we propose an adapted version of the k-core structure for the complete weighted multipartite graph extracted from a deep learning architecture. As a multipartite graph is a combination of bipartite graphs, that are in turn the incidence graphs of hypergraphs, we design k-hypercore decomposition, the hypergraph analogue of k-core degeneracy. We applied k-hypercore to several neural network architectures, more specifically to convolutional neural networks and multilayer perceptrons for image recognition tasks after a very short pretraining. Then we used the information provided by the hypercore numbers of the neurons to re-initialize the weights of the neural network, thus biasing the gradient optimization scheme. Extensive experiments proved that k-hypercore outperforms the state-of-the-art initialization methods.

Revisiting Graph Neural Networks: Graph Filtering Perspective

Hoang Nguyen-Thai, Takanori Maehara, Tsuyoshi Murata

Auto-TLDR; Two-Layers Graph Convolutional Network with Graph Filters Neural Network

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In this work, we develop quantitative results to the learnability of a two-layers Graph Convolutional Network (GCN). Instead of analyzing GCN under some classes of functions, our approach provides a quantitative gap between a two-layers GCN and a two-layers MLP model. From the graph signal processing perspective, we provide useful insights to some flaws of graph neural networks for vertex classification. We empirically demonstrate a few cases when GCN and other state-of-the-art models cannot learn even when true vertex features are extremely low-dimensional. To demonstrate our theoretical findings and propose a solution to the aforementioned adversarial cases, we build a proof of concept graph neural network model with different filters named Graph Filters Neural Network (gfNN).

Unveiling Groups of Related Tasks in Multi-Task Learning

Jordan Frecon, Saverio Salzo, Massimiliano Pontil

Auto-TLDR; Continuous Bilevel Optimization for Multi-Task Learning

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A common approach in multi-task learning is to encourage the tasks to share a low dimensional representation. This has led to the popular method of trace norm regularization, which has proved effective in many applications. In this paper, we extend this approach by allowing the tasks to partition into different groups, within which trace norm regularization is separately applied. We propose a continuous bilevel optimization framework to simultaneously identify groups of related tasks and learn a low dimensional representation within each group. Hinging on recent results on the derivative of generalized matrix functions, we devise a smooth approximation of the upper-level objective via a dual forward-backward algorithm with Bregman distances. This allows us to solve the bilevel problem by a gradient-based scheme. Numerical experiments on synthetic and benchmark datasets support the effectiveness of the proposed method.

Graph Convolutional Neural Networks for Power Line Outage Identification

Jia He, Maggie Cheng

Auto-TLDR; Graph Convolutional Networks for Power Line Outage Identification

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In this paper, we consider the power line outage identification problem as a graph signal classification problem, where the signal at each vertex is given as a time series. We propose graph convolutional networks (GCNs) for the task of classifying signals supported on graphs. An important element of the GCN design is filter design. We consider filtering signals in either the vertex (spatial) domain, or the frequency (spectral) domain. Two basic architectures are proposed. In the spatial GCN architecture, the GCN uses a graph shift operator as the basic building block to incorporate the underlying graph structure into the convolution layer. The spatial filter directly utilizes the graph connectivity information. It defines the filter to be a polynomial in the graph shift operator to obtain the convolved features that aggregate neighborhood information of each node. In the spectral GCN architecture, a frequency filter is used instead. A graph Fourier transform operator first transforms the raw graph signal from the vertex domain to the frequency domain, and then a filter is defined using the graph's spectral parameters. The spectral GCN then uses the output from the graph Fourier transform to compute the convolved features. There are additional challenges to classify the time-evolving graph signal as the signal value at each vertex changes over time. The GCNs are designed to recognize different spatiotemporal patterns from high-dimensional data defined on a graph. The application of the proposed methods to power line outage identification shows that these GCN architectures can successfully classify abnormal signal patterns and identify the outage location.

Unconstrained Vision Guided UAV Based Safe Helicopter Landing

Arindam Sikdar, Abhimanyu Sahu, Debajit Sen, Rohit Mahajan, Ananda Chowdhury

Auto-TLDR; Autonomous Helicopter Landing in Hazardous Environments from Unmanned Aerial Images Using Constrained Graph Clustering

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In this paper, we have addressed the problem of automated detection of safe zone(s) for helicopter landing in hazardous environments from images captured by an Unmanned Aerial Vehicle (UAV). The unconstrained motion of the image capturing drone (the UAV in our case) makes the problem further difficult. The solution pipeline consists of natural landmark detection and tracking, stereo-pair generation using constrained graph clustering, digital terrain map construction and safe landing zone detection. The main methodological contribution lies in mathematically formulating epipolar constraint and then using it in a Minimum Spanning Tree (MST) based graph clustering approach. We have also made publicly available AHL (Autonomous Helicopter Landing) dataset, a new aerial video dataset captured by a drone, with annotated ground-truths. Experimental comparisons with other competing clustering methods i) in terms of Dunn Index and Davies Bouldin Index as well as ii) for frame-level safe zone detection in terms of F-measure and confusion matrix clearly demonstrate the effectiveness of the proposed formulation.

Soft Label and Discriminant Embedding Estimation for Semi-Supervised Classification

Fadi Dornaika, Abdullah Baradaaji, Youssof El Traboulsi

Auto-TLDR; Semi-supervised Semi-Supervised Learning for Linear Feature Extraction and Label Propagation

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In recent times, graph-based semi-supervised learning proved to be a powerful paradigm for processing and mining large datasets. The main advantage relies on the fact that these methods can be useful in propagating a small set of known labels to a large set of unlabeled data. The scarcity of labeled data may affect the performance of the semi-learning. This paper introduces a new semi-supervised framework for simultaneous linear feature extraction and label propagation. The proposed method simultaneously estimates a discriminant transformation and the unknown label by exploiting both labeled and unlabeled data. In addition, the unknowns of the learning model are estimated by integrating two types of graph-based smoothness constraints. The resulting semi-supervised model is expected to learn more discriminative information. Experiments are conducted on six public image datasets. These experimental results show that the performance of the proposed method can be better than that of many state-of-the-art graph-based semi-supervised algorithms.

Feature Extraction by Joint Robust Discriminant Analysis and Inter-Class Sparsity

Fadi Dornaika, Ahmad Khoder

Auto-TLDR; Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA_FSIS)

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Feature extraction methods have been successfully applied to many real-world applications. The classical Linear Discriminant Analysis (LDA) and its variants are widely used as feature extraction methods. Although they have been used for different classification tasks, these methods have some shortcomings. The main one is that the projection axes obtained are not informative about the relevance of original features. In this paper, we propose a linear embedding method that merges two interesting properties: Robust LDA and inter-class sparsity. Furthermore, the targeted projection transformation focuses on the most discriminant original features. The proposed method is called Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA_FSIS). Two kinds of sparsity are explicitly included in the proposed model. The first kind is obtained by imposing the $\ell_{2,1}$ constraint on the projection matrix in order to perform feature ranking. The second kind is obtained by imposing the inter-class sparsity constraint used for getting a common sparsity structure in each class. Comprehensive experiments on five real-world image datasets demonstrate the effectiveness and advantages of our framework over existing linear methods.

Encoding Brain Networks through Geodesic Clustering of Functional Connectivity for Multiple Sclerosis Classification

Muhammad Abubakar Yamin, Valsasina Paola, Michael Dayan, Sebastiano Vascon, Tessadori Jacopo, Filippi Massimo, Vittorio Murino, A Rocca Maria, Diego Sona

Auto-TLDR; Geodesic Clustering of Connectivity Matrices for Multiple Sclerosis Classification

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An important task in brain connectivity research is the classification of patients from healthy subjects. In this work, we present a two-step mathematical framework allowing to discriminate between two groups of people with an application to multiple sclerosis. The proposed approach exploits the properties of the connectivity matrices determined using the covariances between signals of a fixed set of brain areas. These positive semi-definite matrices lay on a Riemannian manifold, allowing to use a geodesic distance defined on this space. In order to generate a vector representation useful for classification purpose, but still preserving the network structures, we encoded the data exploiting the network attractors determined by a geodesic clustering of connectivity matrices. Then clustering centroids were used as a dictionary allowing to encode subject’s connectivity matrices as a vector of geodesic distances. A Linear Support Vector Machine was then used to perform classification between subjects. To demonstrate the advantage of using geodesic metrics in this framework, we conducted the same analysis using Euclidean metric. Experimental results validate the fact that employing geodesic metric in this framework leads to a higher classification performance, whereas with Euclidean metric performance was suboptimal.

One Step Clustering Based on A-Contrario Framework for Detection of Alterations in Historical Violins

Alireza Rezaei, Sylvie Le Hégarat-Mascle, Emanuel Aldea, Piercarlo Dondi, Marco Malagodi

Auto-TLDR; A-Contrario Clustering for the Detection of Altered Violins using UVIFL Images

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Preventive conservation is an important practice in Cultural Heritage. The constant monitoring of the state of conservation of an artwork helps us reduce the risk of damage and number of interventions necessary. In this work, we propose a probabilistic approach for the detection of alterations on the surface of historical violins based on an a-contrario framework. Our method is a one step NFA clustering solution which considers grey-level and spatial density information in one background model. The proposed method is robust to noise and avoids parameter tuning and any assumption about the quantity of the worn out areas. We have used as input UV induced fluorescence (UVIFL) images for considering details not perceivable with visible light. Tests were conducted on image sequences included in the ``Violins UVIFL imagery'' dataset. Results illustrate the ability of the algorithm to distinguish the worn area from the surrounding regions. Comparisons with the state of the art clustering methods shows improved overall precision and recall.

3D Facial Matching by Spiral Convolutional Metric Learning and a Biometric Fusion-Net of Demographic Properties

Soha Sadat Mahdi, Nele Nauwelaers, Philip Joris, Giorgos Bouritsas, Imperial London, Sergiy Bokhnyak, Susan Walsh, Mark Shriver, Michael Bronstein, Peter Claes

Auto-TLDR; Multi-biometric Fusion for Biometric Verification using 3D Facial Mesures

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Face recognition is a widely accepted biometric verification tool, as the face contains a lot of information about the identity of a person. In this study, a 2-step neural-based pipeline is presented for matching 3D facial shape to multiple DNA-related properties (sex, age, BMI and genomic background). The first step consists of a triplet loss-based metric learner that compresses facial shape into a lower dimensional embedding while preserving information about the property of interest. Most studies in the field of metric learning have only focused on Euclidean data. In this work, geometric deep learning is employed to learn directly from 3D facial meshes. To this end, spiral convolutions are used along with a novel mesh-sampling scheme that retains uniformly sampled 3D points at different levels of resolution. The second step is a multi-biometric fusion by a fully connected neural network. The network takes an ensemble of embeddings and property labels as input and returns genuine and imposter scores. Since embeddings are accepted as an input, there is no need to train classifiers for the different properties and available data can be used more efficiently. Results obtained by a 10-fold cross-validation for biometric verification show that combining multiple properties leads to stronger biometric systems. Furthermore, the proposed neural-based pipeline outperforms a linear baseline, which consists of principal component analysis, followed by classification with linear support vector machines and a Naïve Bayes-based score-fuser.

Probabilistic Word Embeddings in Kinematic Space

Adarsh Jamadandi, Rishabh Tigadoli, Ramesh Ashok Tabib, Uma Mudenagudi

Auto-TLDR; Kinematic Space for Hierarchical Representation Learning

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In this paper, we propose a method for learning representations in the space of Gaussian-like distribution defined on a novel geometrical space called Kinematic space. The utility of non-Euclidean geometry for deep representation learning has gained traction, specifically different models of hyperbolic geometry such as Poincar\'{e} and Lorentz models have proven useful for learning hierarchical representations. Going beyond manifolds with constant curvature, albeit has better representation capacity might lead to unhanding of computationally tractable tools like Riemannian optimization methods. Here, we explore a pseudo-Riemannian auxiliary Lorentzian space called Kinematic space and provide a principled approach for constructing a Gaussian-like distribution, which is compatible with gradient-based learning methods, to formulate a probabilistic word embedding framework. Contrary to, mapping lexically distributed representations to a single point vector in Euclidean space, we advocate for mapping entities to density-based representations, as it provides explicit control over the uncertainty in representations. We test our framework by embedding WordNet-Noun hierarchy, a large lexical database, our experiments report strong consistent improvements in Mean Rank and Mean Average Precision (MAP) values compared to probabilistic word embedding frameworks defined on Euclidean and hyperbolic spaces. Our framework reports a significant 83.140\% improvement in Mean Rank compared to Euclidean version and an improvement of 79.416\% over hyperbolic version. Our work serves as an evidence for the utility of novel geometrical spaces for learning hierarchical representations.

On the Global Self-attention Mechanism for Graph Convolutional Networks

Chen Wang, Deng Chengyuan

Auto-TLDR; Global Self-Attention Mechanism for Graph Convolutional Networks

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Applying Global Self-Attention (GSA) mechanism over features has achieved remarkable success on Convolutional Neural Networks (CNNs). However, it is not clear if Graph Convolutional Networks (GCNs) can similarly benefit from such a technique. In this paper, inspired by the similarity between CNNs and GCNs, we study the impact of the Global Self-Attention mechanism on GCNs. We find that consistent with the intuition, the GSA mechanism allows GCNs to capture feature-based vertex relations regardless of edge connections; As a result, the GSA mechanism can introduce extra expressive power to the GCNs. Furthermore, we analyze the impacts of the GSA mechanism on the issues of overfitting and over-smoothing. We prove that the GSA mechanism can alleviate both the overfitting and the over-smoothing issues based on some recent technical developments. Experiments on multiple benchmark datasets illustrate both superior expressive power and less significant overfitting and over-smoothing problems for the GSA-augmented GCNs, which corroborate the intuitions and the theoretical results.

Graph-Based Interpolation of Feature Vectors for Accurate Few-Shot Classification

Yuqing Hu, Vincent Gripon, Stéphane Pateux

Auto-TLDR; Transductive Learning for Few-Shot Classification using Graph Neural Networks

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In few-shot classification, the aim is to learn models able to discriminate classes using only a small number of labeled examples. In this context, works have proposed to introduce Graph Neural Networks (GNNs) aiming at exploiting the information contained in other samples treated concurrently, what is commonly referred to as the transductive setting in the literature. These GNNs are trained all together with a backbone feature extractor. In this paper, we propose a new method that relies on graphs only to interpolate feature vectors instead, resulting in a transductive learning setting with no additional parameters to train. Our proposed method thus exploits two levels of information: a) transfer features obtained on generic datasets, b) transductive information obtained from other samples to be classified. Using standard few-shot vision classification datasets, we demonstrate its ability to bring significant gains compared to other works.

Improved Time-Series Clustering with UMAP Dimension Reduction Method

Clément Pealat, Vincent Cheutet, Guillaume Bouleux

Auto-TLDR; Time Series Clustering with UMAP as a Pre-processing Step

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Clustering is an unsupervised machine learning method giving insights on data without early knowledge. Classes of data are return by assembling similar elements together. Giving the increasing of the available data, this method is now applied in a lot of fields with various data types. Here, we propose to explore the case of time series clustering. Indeed, time series are one of the most classic data type, and are present in various fields such as medical or finance. This kind of data can be pre-processed by of dimension reduction methods, such as the recent UMAP algorithm. In this paper, a benchmark of time series clustering is created, comparing the results with and without UMAP as a pre-processing step. UMAP is used to enhance clustering results. For completeness, three different clustering algorithms and two different geometric representation for the time series (Classic Euclidean geometry, and Riemannian geometry on the Stiefel Manifold) are applied. The results are compared with and without UMAP as a pre-processing step on the databases available at UCR Time Series Classification Archive www.cs.ucr.edu/~eamonn/time_series_data/.

Fast Subspace Clustering Based on the Kronecker Product

Lei Zhou, Xiao Bai, Liang Zhang, Jun Zhou, Edwin Hancock

Auto-TLDR; Subspace Clustering with Kronecker Product for Large Scale Datasets

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Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to subspace clustering, often takes on a sparse representation or a low-rank representation to learn a block diagonal self-representation matrix for subspace generation. However, existing methods require solving a large scale convex optimization problem with a large set of data, with computational complexity reaches O(N^3) for N data points. Therefore, the efficiency and scalability of traditional spectral clustering methods can not be guaranteed for large scale datasets. In this paper, we propose a subspace clustering model based on the Kronecker product. Due to the property that the Kronecker product of a block diagonal matrix with any other matrix is still a block diagonal matrix, we can efficiently learn the representation matrix which is formed by the Kronecker product of k smaller matrices. By doing so, our model significantly reduces the computational complexity to O(kN^{3/k}). Furthermore, our model is general in nature, and can be adapted to different regularization based subspace clustering methods. Experimental results on two public datasets show that our model significantly improves the efficiency compared with several state-of-the-art methods. Moreover, we have conducted experiments on synthetic data to verify the scalability of our model for large scale datasets.

Learning Sparse Deep Neural Networks Using Efficient Structured Projections on Convex Constraints for Green AI

Michel Barlaud, Frederic Guyard

Auto-TLDR; Constrained Deep Neural Network with Constrained Splitting Projection

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In recent years, deep neural networks (DNN) have been applied to different domains and achieved dramatic performance improvements over state-of-the-art classical methods. These performances of DNNs were however often obtained with networks containing millions of parameters and which training required heavy computational power. In order to cope with this computational issue a huge literature deals with proximal regularization methods which are time consuming.\\ In this paper, we propose instead a constrained approach. We provide the general framework for our new splitting projection gradient method. Our splitting algorithm iterates a gradient step and a projection on convex sets. We study algorithms for different constraints: the classical $\ell_1$ unstructured constraint and structured constraints such as the nuclear norm, the $\ell_{2,1} $ constraint (Group LASSO). We propose a new $\ell_{1,1} $ structured constraint for which we provide a new projection algorithm We demonstrate the effectiveness of our method on three popular datasets (MNIST, Fashion MNIST and CIFAR). Experiments on these datasets show that our splitting projection method with our new $\ell_{1,1} $ structured constraint provides the best reduction of memory and computational power. Experiments show that fully connected linear DNN are more efficient for green AI.

2D Discrete Mirror Transform for Image Non-Linear Approximation

Alessandro Gnutti, Fabrizio Guerrini, Riccardo Leonardi

Auto-TLDR; Discrete Mirror Transform (DMT)

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In this paper, a new 2D transform named Discrete Mirror Transform (DMT) is presented. The DMT is computed by decomposing a signal into its even and odd parts around an optimal location in a given direction so that the signal energy is maximally split between the two components. After minimizing the information required to regenerate the original signal by removing redundant structures, the process is iterated leading the signal energy to distribute into a continuously smaller set of coefficients. The DMT can be displayed as a binary tree, where each node represents the single (even or odd) signal derived from the decomposition in the previous level. An optimized version of the DMT (ODMT) is also introduced, by exploiting the possibility to choose different directions at which performing the decomposition. Experimental simulations have been carried out in order to test the sparsity properties of the DMT and ODMT when applied on images: referring to both transforms, the results show a superior performance with respect to the popular Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) in terms of non-linear approximation.

Combined Invariants to Gaussian Blur and Affine Transformation

Jitka Kostkova, Jan Flusser, Matteo Pedone

Auto-TLDR; A new theory of combined moment invariants to Gaussian blur and spatial affine transformation

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The paper presents a new theory of combined moment invariants to Gaussian blur and spatial affine transformation. The blur kernel may be arbitrary oriented, scaled and elongated. No prior information about the kernel parameters and about the underlaying affine transform is required. The main idea, expressed by the Substitution Theorem, is to substitute pure blur invariants into traditional affine moment invariants. Potential applications of the new descriptors are in blur-invariant image recognition and in robust template matching.

Sketch-Based Community Detection Via Representative Node Sampling

Mahlagha Sedghi, Andre Beckus, George Atia

Auto-TLDR; Sketch-based Clustering of Community Detection Using a Small Sketch

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This paper proposes a sketch-based approach to the community detection problem which clusters the full graph through the use of an informative and concise sketch. The reduced sketch is built through an effective sampling approach which selects few nodes that best represent the complete graph and operates on a pairwise node similarity measure based on the average commute time. After sampling, the proposed algorithm clusters the nodes in the sketch, and then infers the cluster membership of the remaining nodes in the full graph based on their aggregate similarity to nodes in the partitioned sketch. By sampling nodes with strong representation power, our approach can improve the success rates over full graph clustering. In challenging cases with large node degree variation, our approach not only maintains competitive accuracy with full graph clustering despite using a small sketch, but also outperforms existing sampling methods. The use of a small sketch allows considerable storage savings, and computational and timing improvements for further analysis such as clustering and visualization. We provide numerical results on synthetic data based on the homogeneous, heterogeneous and degree corrected versions of the stochastic block model, as well as experimental results on real-world data.

Content-Sensitive Superpixels Based on Adaptive Regrowth

Xiaopeng Li, Junlin Xiong

Auto-TLDR; Adaptive Regrowth for Content-Sensitive Superpixels

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In this paper, we propose an efficient method to produce content-sensitive superpixels. Our method produces regular superpixels in relatively homogeneous regions and captures object boundaries in content-dense regions. Compared with the existing content-sensitive superpixel methods,a new adaptive regrowth strategy with an explicit boundary constraint is proposed.The boundary constraint limits the shapes and the sizes of superpixels to ensure semantic consistency. The adaptive regrowth strategy generates more superpixels to capture small objects in content-dense regions. Experiments on the BSDS500 benchmark show that our method outperforms the state-of-the-art superpixel methods in terms of content sensitivity and several standard evaluation metrics.

Learning Connectivity with Graph Convolutional Networks

Hichem Sahbi

Auto-TLDR; Learning Graph Convolutional Networks Using Topological Properties of Graphs

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Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing convolutional operations to arbitrary non-regular domains. In particular, GCNs operating on spatial domains show superior performances compared to spectral ones, however their success is highly dependent on how the topology of input graphs is defined. In this paper, we introduce a novel framework for graph convolutional networks that learns the topological properties of graphs. The design principle of our method is based on the optimization of a constrained objective function which learns not only the usual convolutional parameters in GCNs but also a transformation basis that conveys the most relevant topological relationships in these graphs. Experiments conducted on the challenging task of skeleton-based action recognition shows the superiority of the proposed method compared to handcrafted graph design as well as the related work.

Kernel-based Graph Convolutional Networks

Hichem Sahbi

Auto-TLDR; Spatial Graph Convolutional Networks in Recurrent Kernel Hilbert Space

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Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing deep learning to arbitrary non-regular domains. Most of the existing GCNs follow a neighborhood aggregation scheme, where the representation of a node is recursively obtained by aggregating its neighboring node representations using averaging or sorting operations. However, these operations are either ill-posed or weak to be discriminant or increase the number of training parameters and thereby the computational complexity and the risk of overfitting. In this paper, we introduce a novel GCN framework that achieves spatial graph convolution in a reproducing kernel Hilbert space. The latter makes it possible to design, via implicit kernel representations, convolutional graph filters in a high dimensional and more discriminating space without increasing the number of training parameters. The particularity of our GCN model also resides in its ability to achieve convolutions without explicitly realigning nodes in the receptive fields of the learned graph filters with those of the input graphs, thereby making convolutions permutation agnostic and well defined. Experiments conducted on the challenging task of skeleton-based action recognition show the superiority of the proposed method against different baselines as well as the related work.

Anime Sketch Colorization by Component-Based Matching Using Deep Appearance Features and Graph Representation

Thien Do, Pham Van, Anh Nguyen, Trung Dang, Quoc Nguyen, Bach Hoang, Giao Nguyen

Auto-TLDR; Combining Deep Learning and Graph Representation for Sketch Colorization

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Sketch colorization is usually expensive and time-consuming for artists, and automating this process can have many pragmatic applications in the animation, comic book, and video game industry. However, automatic image colorization faces many challenges, because sketches not only lack texture information but also potentially entail complicated objects that require acute coloring. These difficulties usually result in incorrect color assignments that can ruin the aesthetic appeal of the final output. In this paper, we present a novel component-based matching framework that combines deep learned features and quadratic programming {\color{red} with a new cost function} to solve this colorization problem. The proposed framework inputs a character's sketches as well as a colored image in the same cut of a movie, and outputs a high-quality sequence of colorized frames based on the color assignment in the reference colored image. To carry out this colorization task, we first utilize a pretrained ResNet-34 model to extract elementary components' features to match certain pairs of components (one component from the sketch and one from reference). Next, a graph representation is constructed in order to process and match the remaining components that could not be done in the first step. Since the first step has reduced the number of components to be matched by the graph, we can solve this graph problem in a short computing time even when there are hundreds of different components present in each sketch. We demonstrate the effectiveness of the proposed solution by conducting comprehensive experiments and producing aesthetically pleasing results. To the best of our knowledge, our framework is the first work that combines deep learning and graph representation to colorize anime and achieves a high pixel-level accuracy at a reasonable time cost.

Classification of Intestinal Gland Cell-Graphs Using Graph Neural Networks

Linda Studer, Jannis Wallau, Heather Dawson, Inti Zlobec, Andreas Fischer

Auto-TLDR; Graph Neural Networks for Classification of Dysplastic Gland Glands using Graph Neural Networks

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We propose to classify intestinal glands as normal or dysplastic using cell-graphs and graph-based deep learning methods. Dysplastic intestinal glands can lead to colorectal cancer, which is one of the three most common cancer types in the world. In order to assess the cancer stage and thus the treatment of a patient, pathologists analyse tissue samples of affected patients. Among other factors, they look at the changes in morphology of different tissues, such as the intestinal glands. Cell-graphs have a high representational power and can describe topological and geometrical properties of intestinal glands. However, classical graph-based methods have a high computational complexity and there is only a limited range of machine learning methods available. In this paper, we propose Graph Neural Networks (GNNs) as an efficient learning-based approach to classify cell-graphs. We investigate different variants of so-called Message Passing Neural Networks and compare them with a classical graph-based approach based on approximated Graph Edit Distance and k-nearest neighbours classifier. A promising classification accuracy of 94.1% is achieved by the proposed method on the pT1 Gland Graph dataset, which is an increase of 11.5% over the baseline result.

Force Banner for the Recognition of Spatial Relations

Robin Deléarde, Camille Kurtz, Laurent Wendling, Philippe Dejean

Auto-TLDR; Spatial Relation Recognition using Force Banners

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Studying the spatial organization of objects in images is fundamental to increase both the understanding of the sensed scene and the accuracy of the perceived similarity between images. This often leads to the problem of spatial relation recognition: given two objects depicted in an image, what is their spatial relation? In this article, we consider this as a classification problem. Instead of considering directly the original image space (or imaging features) to predict the spatial relation, we propose a novel intermediate representation (called Force Banner) modeling rich spatial information between pairs of objects composing a scene. Such a representation captures the relative position between objects using a panel of forces (attraction and repulsion), that take into account the structural shapes of the objects and their distance in a directional fashion. Force Banners are used to feed a classical 2D Convolutional Neural Network (CNN) for the recognition of spatial relations, benefiting from pre-trained models and fine-tuning. Experimental results obtained on a dataset of images with various shapes highlight the interest of this approach, and in particular its benefit to describe spatial information.

Cluster-Size Constrained Network Partitioning

Maksim Mironov, Konstantin Avrachenkov

Auto-TLDR; Unsupervised Graph Clustering with Stochastic Block Model

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In this paper we consider a graph clustering problem with a given number of clusters and approximate desired sizes of the clusters. One possible motivation for such task could be the problem of databases or servers allocation within several given large computational clusters, where we want related objects to share the same cluster in order to minimize latency and transaction costs. This task differs from the original community detection problem, though we adopt some ideas from Glauber Dynamics and Label Propagation Algorithm. At the same time we consider no additional information about node labels, so the task has nature of unsupervised learning. We propose an algorithm for the problem, show that it works well for a large set of parameters of Stochastic Block Model (SBM) and theoretically show its running time complexity for achieving almost exact recovery is of $O(n\cdot\deg_{av} \cdot \omega )$ for the mean-field SBM with $\omega$ tending to infinity arbitrary slow. Other significant advantage of the proposed approach is its local nature, which means it can be efficiently distributed with no scheduling or synchronization.

Supervised Classification Using Graph-Based Space Partitioning for Multiclass Problems

Nicola Yanev, Ventzeslav Valev, Adam Krzyzak, Karima Ben Suliman

Auto-TLDR; Box Classifier for Multiclass Classification

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We introduce and investigate in multiclass setting an efficient classifier which partitions the training data by means of multidimensional parallelepipeds called boxes. We show that multiclass classification problem at hand can be solved by integrating the heuristic minimum clique cover approach and the k-nearest neighbor rule. Our algorithm is motivated an algorithm for partitioning a graph into a minimal number of maximal. The main advantage of the new classifier called Box classifier is that it optimally utilizes the geometrical structure of the training set by decomposing the l-class problem (l > 2) into l binary classification problems. We discuss computational complexity of the proposed Box classifier. The extensive experiments performed on the simulated and real data for binary and multiclass problems show that in almost all cases the Box classifier performs significantly better than k-NN, SVM and decision trees.

A Riemannian Framework for Detecting Stimulus-Relevant Fiber Pathways

Jingyong Su, Linlin Tang, Zhipeng Yang, Mengmeng Guo

Auto-TLDR; Clustering Task-Specific Fiber Pathways in Functional MRI using BOLD Signals

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Functional MRI based on blood oxygenation level-dependent (BOLD) contrast is well established as a neuro-imaging technique for detecting neural activity in the cortex of the human brain. Recent studies have shown that variations of BOLD signals in white matter are also related to neural activities both in resting state and under functional loading. We develop a comprehensive framework of detecting task-specific fiber pathways. We not only study fiber tracts as open curves with different physical features (shape, scale, orientation and position), but also incorporate the BOLD signals transmitted along them to find stimulus-relevant pathways. Specifically, we propose a novel Riemannian metric, which is a weighted sum of distances in product space of shapes and functions. This metric provides both a cost function for registration and a proper distance for comparison. Experimental results on real data have shown that we can cluster fiber pathways correctly by evaluating correlations between BOLD signals and stimuli, temporal variations and power spectra of them. The proposed framework can also be easily generalized to various applications where multi-modality data exist.

Motion Segmentation with Pairwise Matches and Unknown Number of Motions

Federica Arrigoni, Tomas Pajdla, Luca Magri

Auto-TLDR; Motion Segmentation using Multi-Modelfitting andpermutation synchronization

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In this paper we address motion segmentation, that is the problem of clustering points in multiple images according to a number of moving objects. Two-frame correspondences are assumed as input without prior knowledge about trajectories. Our method is based on principles from ''multi-model fitting'' and ''permutation synchronization'', and - differently from previous techniques working under the same assumptions - it can handle an unknown number of motions. The proposed approach is validated on standard datasets, showing that it can correctly estimate the number of motions while maintaining comparable or better accuracy than the state of the art.

Supervised Domain Adaptation Using Graph Embedding

Lukas Hedegaard, Omar Ali Sheikh-Omar, Alexandros Iosifidis

Auto-TLDR; Domain Adaptation from the Perspective of Multi-view Graph Embedding and Dimensionality Reduction

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Getting deep convolutional neural networks to perform well requires a large amount of training data. When the available labelled data is small, it is often beneficial to use transfer learning to leverage a related larger dataset (source) in order to improve the performance on the small dataset (target). Among the transfer learning approaches, domain adaptation methods assume that distributions between the two domains are shifted and attempt to realign them. In this paper, we consider the domain adaptation problem from the perspective of multi-view graph embedding and dimensionality reduction. Instead of solving the generalised eigenvalue problem to perform the embedding, we formulate the graph-preserving criterion as loss in the neural network and learn a domain-invariant feature transformation in an end-to-end fashion. We show that the proposed approach leads to a powerful Domain Adaptation framework which generalises the prior methods CCSA and d-SNE, and enables simple and effective loss designs; an LDA-inspired instantiation of the framework leads to performance on par with the state-of-the-art on the most widely used Domain Adaptation benchmarks, Office31 and MNIST to USPS datasets.