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Generalized Conics: Properties and Applications

Aysylu Gabdulkhakova, Walter Kropatsch

Auto-TLDR; A Generalized Conic Representation for Distance Fields

Abstract Slides Poster

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.

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Exact and Convergent Iterative Methods to Compute the Orthogonal Point-To-Ellipse Distance

Siyu Guo, Pingping Hu, Zhigang Ling, He Wen, Min Liu, Lu Tang

Auto-TLDR; Convergent iterative algorithm for orthogonal distance based ellipse fitting

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Computation of the orthogonal distance from a given point to an ellipse is the basis of orthogonal distance based ellipse fitting methods. The problem of this orthogonal distance and the corresponding orthogonal contacting point on the ellipse is investigated, and two algorithms, the exact one and the convergent iterative one, are proposed. The exact algorithm utilizes the closed form solution of quartic equations, but is numerically unstable. The iterative algorithm, however, uses Newton’s method to solve the equation, and starts from an initial solution that is proven to lead to a convergent iteration. The proposed algorithms are compared in experiments with an existing rival. Although the rival algorithm is slightly faster and more accurate in realistic scenarios, divergence is likely to occur. On the other hand, both our exact and iterative algorithms can reliably produce the solution needed. While the exact algorithm encounters numeric instability, the iterative algorithm is only slightly outperformed by the existing rival in speed and accuracy, but at the same time provides more reliable computation process, thus making it a preferable method for the task.

A Hybrid Metric Based on Persistent Homology and Its Application to Signal Classification

Austin Lawson, Yu-Min Chung, William Cruse

Auto-TLDR; Topological Data Analysis with Persistence Curves

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Topological Data Analysis (TDA) is a rising field in machine learning. TDA considers the shape of data set. Persistence diagrams, one of main tools in TDA, store topological information about the data. Persistence curves, a recently developed framework, provides a canonical and flexible way to encode the information presented in persistence diagrams into vectors. Based on persistence curves, we (1) provide new sets of features for time series, (2) prove that these features are robust to noise, (3) propose a hybrid metric that takes both geometric and topological information of the time series into account. Finally, we apply these metrics to the UCR Time Series Classification Archive. These empirical results show that our metrics perform better than the relevant benchmark in most cases.

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.

Camera Calibration Using Parallel Line Segments

Gaku Nakano

Auto-TLDR; Closed-Form Calibration of Surveillance Cameras using Parallel 3D Line Segment Projections

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This paper proposes a camera calibration method suitable for surveillance cameras using the image projection of parallel 3D line segments of the same length. We assume that vertical line segments are perpendicular to the ground plane and their bottom end-points are on the ground plane. Under this assumption, the camera parameters can be directly solved by at least two line segments without estimating vanishing points. Extending the minimal solution, we derive a closed-form solution to the least squares case with more than two line segments. Lens distortion is jointly optimized in bundle adjustment. Synthetic data evaluation shows that the best depression angle of a camera is around 50 degrees. In real data evaluation, we use body joints of pedestrians as vertical line segments. The experimental results on publicly available datasets show that the proposed method with a human pose detector can correctly calibrate wide-angle cameras including radial distortion.

A Globally Optimal Method for the PnP Problem with MRP Rotation Parameterization

Manolis Lourakis, George Terzakis

Auto-TLDR; A Direct least squares, algebraic PnP solver with modified Rodrigues parameters

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The perspective-n-point (PnP) problem is of fundamental importance in computer vision. A global optimality condition for PnP that is independent of a particular rotation parameterization was recently developed by Nakano. This paper puts forward a direct least squares, algebraic PnP solution that extends Nakano's work by combining his optimality condition with the modified Rodrigues parameters (MRPs) for parameterizing rotation. The result is a system of polynomials that is solved using the Groebner basis approach. An MRP vector has twice the rotational range of the classical Rodrigues (i.e., Cayley) vector used by Nakano to represent rotation. The proposed solver provides strong guarantees that the full rotation singularity associated with MRPs is avoided. Furthermore, detailed experiments provide evidence that our solver attains accuracy that is indistinguishable from Nakano's Cayley-based solution with a moderate increase in computational cost.

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.

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.

Generic Document Image Dewarping by Probabilistic Discretization of Vanishing Points

Gilles Simon, Salvatore Tabbone

Auto-TLDR; Robust Document Dewarping using vanishing points

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Document images dewarping is still a challenge especially when documents are captured with one camera in an uncontrolled environment. In this paper we propose a generic approach based on vanishing points (VP) to reconstruct the 3D shape of document pages. Unlike previous methods we do not need to segment the text included in the documents. Therefore, our approach is less sensitive to pre-processing and segmentation errors. The computation of the VPs is robust and relies on the a-contrario framework, which has only one parameter whose setting is based on probabilistic reasoning instead of experimental tuning. Thus, our method can be applied to any kind of document including text and non-text blocks and extended to other kind of images. Experimental results show that the proposed method is robust to a variety of distortions.

Computing Stable Resultant-Based Minimal Solvers by Hiding a Variable

Snehal Bhayani, Zuzana Kukelova, Janne Heikkilä

Auto-TLDR; Sparse Permian-Based Method for Solving Minimal Systems of Polynomial Equations

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Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e., solving minimal problems, in a RANSAC-style framework. Minimal problems often result in complex systems of polynomial equations. The existing state-of-the-art methods for solving such systems are either based on Groebner Basis and the action matrix method, which have been extensively studied and optimized in the recent years or recently proposed approach based on a resultant computation using an extra variable. In this paper, we study an interesting alternative resultant-based method for solving sparse systems of polynomial equations by hiding one variable. This approach results in a larger eigenvalue problem than the action matrix and extra variable resultant-based methods; however, it does not need to compute an inverse or elimination of large matrices that may be numerically unstable. The proposed approach includes several improvements to the standard sparse resultant algorithms, which significantly improves the efficiency and stability of the hidden variable resultant-based solvers as we demonstrate on several interesting computer vision problems. We show that for the studied problems, our sparse resultant based approach leads to more stable solvers than the state-of-the-art Groebner Basis as well as existing resultant-based solvers, especially in close to critical configurations. Our new method can be fully automated and incorporated into existing tools for the automatic generation of efficient minimal solvers.

Graph Signal Active Contours

Olivier Lezoray

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

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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.

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.

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.

3D Pots Configuration System by Optimizing Over Geometric Constraints

Jae Eun Kim, Muhammad Zeeshan Arshad, Seong Jong Yoo, Je Hyeong Hong, Jinwook Kim, Young Min Kim

Auto-TLDR; Optimizing 3D Conﬁgurations for Stable Pottery Restoration from irregular and noisy evidence

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While potteries are common artifacts excavated in archaeological sites, the restoration process relies on the manual cleaning and reassembling shattered pieces. Since the number of possible 3D conﬁgurations is considerably large, the exhaustive manual trial may result in an abrasion on fractured surfaces and even failure to ﬁnd the correct matches. As a result, many recent works suggest virtual reassembly from 3D scans of the fragments. The problem is challenging in the view of the conventional 3D geometric analysis, as it is hard to extract reliable shape features from the thin break lines. We propose to optimize the global conﬁguration by combining geometric constraints with information from noisy shape features. Speciﬁcally, we enforce bijection and continuity of sequence of correspondences given estimates of corners and pair-wise matching scores between multiple break lines. We demonstrate that our pipeline greatly increases the accuracy of correspondences, resulting in the stable restoration of 3D conﬁgurations from irregular and noisy evidence.

Learning Graph Matching Substitution Weights Based on a Linear Regression

Shaima Algabli, Francesc Serratosa

Auto-TLDR; Learning the weights on local attributes of attributed graphs

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Attributed graphs are structures that are useful to represent objects through the information of their local parts and their relations. Each characteristic in the local parts is represented by different attributes on the nodes. In this context, the comparison between structured objects is performed through a distance between attributed graphs. If we want to correctly tune the distance and the node correspondence between graphs, we have to add some weights on the node attributes to gauge the importance of each local characteristic. In this paper, we present a method to learn the weights on each node attribute. It is based on building an embedded space and imposing the weights we want to learn to be the constants of the hyperplane deduced by a linear regression applied on a cloud of points. These points represent the node-to-node mappings.

Boundaries of Single-Class Regions in the Input Space of Piece-Wise Linear Neural Networks

Jay Hoon Jung, Youngmin Kwon

Auto-TLDR; Piece-wise Linear Neural Networks with Linear Constraints

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An input space is a set of all the possible inputs for a neural network. An element or a group of elements in the input space can easily be understood by projecting them on their original forms. Even though Piece-wise Linear Neural Networks (PLNNs) are a nonlinear system in general, a PLNN can also be expressed in terms of linear constraints because the Rectified Linear Units (ReLU) function is a piece-wise linear function. A PLNN divides the input space into disjoint linear regions. We proved that all components of the outputs are continuous at the boundary between two different adjacent regions. This continuity implies that the boundary corresponding to a unit itself should be continuous regardless of the regions. Furthermore, we also obtained the boundaries of a single-class region, which has the same predicted classes in the interior of the region. Finally, we suggested that the point-wise robustness of a neural network can be calculated by investigating the boundaries of linear regions and the single-class regions. We obtained adversarial examples in which Euclidean distances from original inputs are less than 0.01 pixels.

Transferable Model for Shape Optimization subject to Physical Constraints

Lukas Harsch, Johannes Burgbacher, Stefan Riedelbauch

Auto-TLDR; U-Net with Spatial Transformer Network for Flow Simulations

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The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture is used to learn the underlying physical behaviour of fluid flows. The network is used to infer the solution of flow simulations which will be shown for a wide range of generic channel flow simulations. Physical meaningful quantities can be computed on the obtained solution, e.g. the total pressure difference or the forces on the objects. A Spatial Transformer Network with thin-plate-splines is used for the interaction between the physical constraints and the geometric representation of the objects. Thus, a transformation from an initial to a target geometry is performed such that the object is fulfilling the given constraints. This method is fully differentiable i.e., gradient informations can be used for the transformation. This can be seen as an inverse design process. The advantage of this method over many other proposed methods is, that the physical constraints are based on the inferred flow field solution. Thus, we can apply a transferable model to varying problem setups, which is not limited to a given set of geometry parameters or physical quantities.

Uniform and Non-Uniform Sampling Methods for Sub-Linear Time K-Means Clustering

Yuanhang Ren, Ye Du

Auto-TLDR; Sub-linear Time Clustering with Constant Approximation Ratio for K-Means Problem

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The $k$-means problem is arguably the most well-known clustering problem in machine learning, and lots of approximation algorithms have been proposed for it. However, many of these algorithms may become infeasible when data is huge. Sub-linear time algorithms with constant approximation ratios are desirable in this scenario. In this paper, we first improve the analysis of the algorithm proposed by \cite{Mohan:2017:BNA:3172077.3172235} by sharpening the approximation ratio from $4(\alpha+\beta)$ to $\alpha+\beta$. Moreover, on mild assumptions of the data, a constant approximation ratio can be achieved in poly-logarithmic time by the algorithm. Furthermore, we propose a novel sub-linear time clustering algorithm called {\it Double-K-M$\text{C}^2$ sampling} as well. Experiments on the data clustering task and the image segmentation task have validated the effectiveness of our algorithms.

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.

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.

Calibration and Absolute Pose Estimation of Trinocular Linear Camera Array for Smart City Applications

Martin Ahrnbom, Mikael Nilsson, Håkan Ardö, Kalle Åström, Oksana Yastremska-Kravchenko, Aliaksei Laureshyn

Auto-TLDR; Trinocular Linear Camera Array Calibration for Traffic Surveillance Applications

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A method for calibrating a Trinocular Linear Camera Array (TLCA) for traffic surveillance applications, such as towards smart cities, is presented. A TLCA-specific parametrization guarantees that the calibration finds a model where all the cameras are on a straight line. The method uses both a chequerboard close to the camera, as well as measured 3D points far from the camera: points measured in world coordinates, as well as their corresponding 2D points found manually in the images. Superior calibration accuracy can be obtained compared to standard methods using only a single data source, largely due to the use of chequerboards, while the line constraint in the parametrization allows for joint rectification. The improved triangulation accuracy, from 8-12 cm to around 6 cm when calibrating with 30-50 points in our experiment, allowing better road user analysis. The method is demonstrated by a proof-of-concept application where a point cloud is generated from multiple disparity maps, visualizing road user detections in 3D.

A Hierarchical Framework for Leaf Instance Segmentation: Application to Plant Phenotyping

Swati Bhugra, Kanish Garg, Santanu Chaudhury, Brejesh Lall

Auto-TLDR; Under-segmentation of plant image using a graph based formulation to extract leaf shape knowledge for the task of leaf instance segmentation

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Image based analysis of plants is a high-throughput and non-invasive approach to study plant traits. Based on plant image data, the quantitative estimation of many plant traits (leaf area index, biomass etc.) is associated with accurate segmentation of individual leaves. However, this task is challenging due to the presence of overlapped leaves and lack of discernible boundaries between them. In addition, variability in leaf shapes and arrangement among different plant species limits the broad utilisation of current leaf instance segmentation algorithms. In this paper, we propose a novel framework that relies on under-segmentation of plant image using a graph based formulation to extract leaf shape knowledge for the task of leaf instance segmentation. These shape priors are generated based on leaf shape characteristics independent of plant species. We demonstrate the performance of the proposed framework across multiple plant dataset i.e. Arabidopsis, Komatsuna and Salad. Experimental results indicate its broad utility.

Minimal Solvers for Indoor UAV Positioning

Marcus Valtonen Örnhag, Patrik Persson, Mårten Wadenbäck, Kalle Åström, Anders Heyden

Auto-TLDR; Relative Pose Solvers for Visual Indoor UAV Navigation

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In this paper we consider a collection of relative pose problems which arise naturally in applications for visual indoor UAV navigation. We focus on cases where additional information from an onboard IMU is available and thus provides a partial extrinsic calibration through the gravitational vector. The solvers are designed for a partially calibrated camera, for a variety of realistic indoor scenarios, which makes it possible to navigate using images of the ground floor. Current state-of-the-art solvers use more general assumptions, such as using arbitrary planar structures; however, these solvers do not yield adequate reconstructions for real scenes, nor do they perform fast enough to be incorporated in real-time systems. We show that the proposed solvers enjoy better numerical stability, are faster, and require fewer point correspondences, compared to state-of-the-art solvers. These properties are vital components for robust navigation in real-time systems, and we demonstrate on both synthetic and real data that our method outperforms other methods, and yields superior motion estimation.

Classification of Spatially Enriched Pixel Time Series with Convolutional Neural Networks

Mohamed Chelali, Camille Kurtz, Anne Puissant, Nicole Vincent

Auto-TLDR; Spatio-Temporal Features Extraction from Satellite Image Time Series Using Random Walk

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Satellite Image Time Series (SITS), MRI sequences, and more generally image time series, constitute 2D+t data providing spatial and temporal information about an observed scene. Given a pattern recognition task such as image classification, considering jointly such rich information is crucial during the decision process. Nevertheless, due to the complex representation of the data-cube, spatio-temporal features extraction from 2D+t data remains difficult to handle. We present in this article an approach to learn such features from this data, and then to proceed to their classification. Our strategy consists in enriching pixel time series with spatial information. It is based on Random Walk to build a novel segment-based representation of the data, passing from a 2D+t dimension to a 2D one, without loosing too much spatial information. Such new representation is then involved in an end-to-end learning process with a classical 2D Convolutional Neural Network (CNN) in order to learn spatio-temporal features for the classification of image time series. Our approach is evaluated on a remote sensing application for the mapping of agricultural crops. Thanks to a visual attention mechanism, the proposed $2D$ spatio-temporal representation makes also easier the interpretation of a SITS to understand spatio-temporal phenomenons related to soil management practices.

An Invariance-Guided Stability Criterion for Time Series Clustering Validation

Florent Forest, Alex Mourer, Mustapha Lebbah, Hanane Azzag, Jérôme Lacaille

Auto-TLDR; An invariance-guided method for clustering model selection in time series data

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Time series clustering is a challenging task due to the specificities of this type of data. Temporal correlation and invariance to transformations such as shifting, warping or noise prevent the use of standard data mining methods. Time series clustering has been mostly studied under the angle of finding efficient algorithms and distance metrics adapted to the specific nature of time series data. Much less attention has been devoted to the general problem of model selection. Clustering stability has emerged as a universal and model-agnostic principle for clustering model selection. This principle can be stated as follows: an algorithm should find a structure in the data that is resilient to perturbation by sampling or noise. We propose to apply stability analysis to time series by leveraging prior knowledge on the nature and invariances of the data. These invariances determine the perturbation process used to assess stability. Based on a recently introduced criterion combining between-cluster and within-cluster stability, we propose an invariance-guided method for model selection, applicable to a wide range of clustering algorithms. Experiments conducted on artificial and benchmark data sets demonstrate the ability of our criterion to discover structure and select the correct number of clusters, whenever data invariances are known beforehand.

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.

Interactive Style Space of Deep Features and Style Innovation

Bingqing Guo, Pengwei Hao

Auto-TLDR; Interactive Style Space of Convolutional Neural Network Features

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Stylizing images as paintings has been a popular computer vision technique for a long time. However, most studies only consider the art styles known today, and rarely have investigated styles that have not been painted yet. We fill this gap by projecting the high-dimensional style space of Convolutional Neural Network features to the latent low-dimensional style manifold space. It is worth noting that in our visualized space, simple style linear interpolation is enabled to generate new artistic styles that would revolutionize the future of art in technology. We propose a model of an Interactive Style Space (ISS) to prove that in a manifold style space, the unknown styles are obtainable through interpolation of known styles. We verify the correctness and feasibility of our Interactive Style Space (ISS) and validate style interpolation within the space.

Generic Merging of Structure from Motion Maps with a Low Memory Footprint

Gabrielle Flood, David Gillsjö, Patrik Persson, Anders Heyden, Kalle Åström

Auto-TLDR; A Low-Memory Footprint Representation for Robust Map Merge

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With the development of cheap image sensors, the amount of available image data have increased enormously, and the possibility of using crowdsourced collection methods has emerged. This calls for development of ways to handle all these data. In this paper, we present new tools that will enable efficient, flexible and robust map merging. Assuming that separate optimisations have been performed for the individual maps, we show how only relevant data can be stored in a low memory footprint representation. We use these representations to perform map merging so that the algorithm is invariant to the merging order and independent of the choice of coordinate system. The result is a robust algorithm that can be applied to several maps simultaneously. The result of a merge can also be represented with the same type of low-memory footprint format, which enables further merging and updating of the map in a hierarchical way. Furthermore, the method can perform loop closing and also detect changes in the scene between the capture of the different image sequences. Using both simulated and real data — from both a hand held mobile phone and from a drone — we verify the performance of the proposed method.

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.

Inferring Functional Properties from Fluid Dynamics Features

Andrea Schillaci, Maurizio Quadrio, Carlotta Pipolo, Marcello Restelli, Giacomo Boracchi

Auto-TLDR; Exploiting Convective Properties of Computational Fluid Dynamics for Medical Diagnosis

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In a wide range of applied problems involving fluid flows, Computational Fluid Dynamics (CFD) provides detailed quantitative information on the flow field, at various levels of fidelity and computational cost. However, CFD alone cannot predict high-level functional properties of the system that are not easily obtained from the equations of fluid motion. In this work, we present a data-driven framework to extract additional information, such as medical diagnostic output, from CFD solutions. The task is made difficult by the huge data dimensionality of CFD, together with the limited amount of training data implied by its high computational cost. By pursuing a traditional ML pipeline of pre-processing, feature extraction, and model training, we demonstrate that informative features can be extracted from CFD data. Two experiments, pertaining to different application domains, support the claim that the convective properties implicit into a CFD solution can be leveraged to retrieve functional information for which an analytical definition is missing. Despite the preliminary nature of our study and the relative simplicity of both the geometrical and CFD models, for the first time we demonstrate that the combination of ML and CFD can diagnose a complex system in terms of high-level functional information.

PIF: Anomaly detection via preference embedding

Filippo Leveni, Luca Magri, Giacomo Boracchi, Cesare Alippi

Auto-TLDR; PIF: Anomaly Detection with Preference Embedding for Structured Patterns

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We address the problem of detecting anomalies with respect to structured patterns. To this end, we conceive a novel anomaly detection method called PIF, that combines the advantages of adaptive isolation methods with the flexibility of preference embedding. Specifically, we propose to embed the data in a high dimensional space where an efficient tree-based method, PI-FOREST, is employed to compute an anomaly score. Experiments on synthetic and real datasets demonstrate that PIF favorably compares with state-of-the-art anomaly detection techniques, and confirm that PI-FOREST is better at measuring arbitrary distances and isolate points in the preference space.

Learning Embeddings for Image Clustering: An Empirical Study of Triplet Loss Approaches

Kalun Ho, Janis Keuper, Franz-Josef Pfreundt, Margret Keuper

Auto-TLDR; Clustering Objectives for K-means and Correlation Clustering Using Triplet Loss

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In this work, we evaluate two different image clustering objectives, k-means clustering and correlation clustering, in the context of Triplet Loss induced feature space embeddings. Specifically, we train a convolutional neural network to learn discriminative features by optimizing two popular versions of the Triplet Loss in order to study their clustering properties under the assumption of noisy labels. Additionally, we propose a new, simple Triplet Loss formulation, which shows desirable properties with respect to formal clustering objectives and outperforms the existing methods. We evaluate all three Triplet loss formulations for K-means and correlation clustering on the CIFAR-10 image classification dataset.

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.

Fractional Adaptation of Activation Functions in Neural Networks

Julio Zamora Esquivel, Jesus Adan Cruz Vargas, Paulo Lopez-Meyer, Hector Alfonso Cordourier Maruri, Jose Rodrigo Camacho Perez, Omesh Tickoo

Auto-TLDR; Automatic Selection of Activation Functions in Neural Networks using Fractional Calculus

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In this work, we introduce a generalization methodology for the automatic selection of the activation functions inside a neural network, taking advantage of concepts defined in fractional calculus. This methodology enables the neural network to search and optimize its own activation functions during the training process, by defining the fractional order of the derivative of a given primitive activation function. This fractional order is tuned as an additional training hyper-parameter a for intrafamily selection and b for cross family selection. By following this approach, the neurons inside the network can adjust their activation functions, e.g. from MLP to RBF networks, to best fit the input data, and reduce the output error. The experimental results obtained show the benefits of using this technique implemented on a ResNet18 topology, by outperforming the accuracy of a ResNet100 trained with CIFAR10 and Improving 1% ImageNet reported in the literature.

Holistic Grid Fusion Based Stop Line Estimation

Runsheng Xu, Faezeh Tafazzoli, Li Zhang, Timo Rehfeld, Gunther Krehl, Arunava Seal

Auto-TLDR; Fused Multi-Sensory Data for Stop Lines Detection in Intersection Scenarios

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Intersection scenarios provide the most complex traffic situations in Autonomous Driving and Driving Assistance Systems. Knowing where to stop in advance in an intersection is an essential parameter in controlling the longitudinal velocity of the vehicle. Most of the existing methods in literature solely use cameras to detect stop lines, which is typically not sufficient in terms of detection range. To address this issue, we propose a method that takes advantage of fused multi-sensory data including stereo camera and lidar as input and utilizes a carefully designed convolutional neural network architecture to detect stop lines. Our experiments show that the proposed approach can improve detection range compared to camera data alone, works under heavy occlusion without observing the ground markings explicitly, is able to predict stop lines for all lanes and allows detection at a distance up to 50 meters.

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.

Weakly Supervised Geodesic Segmentation of Egyptian Mummy CT Scans

Avik Hati, Matteo Bustreo, Diego Sona, Vittorio Murino, Alessio Del Bue

Auto-TLDR; A Weakly Supervised and Efficient Interactive Segmentation of Ancient Egyptian Mummies CT Scans Using Geodesic Distance Measure and GrabCut

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In this paper, we tackle the task of automatically analyzing 3D volumetric scans obtained from computed tomography (CT) devices. In particular, we address a particular task for which data is very limited: the segmentation of ancient Egyptian mummies CT scans. We aim at digitally unwrapping the mummy and identify different segments such as body, bandages and jewelry. The problem is complex because of the lack of annotated data for the different semantic regions to segment, thus discouraging the use of strongly supervised approaches. We, therefore, propose a weakly supervised and efficient interactive segmentation method to solve this challenging problem. After segmenting the wrapped mummy from its exterior region using histogram analysis and template matching, we first design a voxel distance measure to find an approximate solution for the body and bandage segments. Here, we use geodesic distances since voxel features as well as spatial relationship among voxels is incorporated in this measure. Next, we refine the solution using a GrabCut based segmentation together with a tracking method on the slices of the scan that assigns labels to different regions in the volume, using limited supervision in the form of scribbles drawn by the user. The efficiency of the proposed method is demonstrated using visualizations and validated through quantitative measures and qualitative unwrapping of the mummy.

Trainable Spectrally Initializable Matrix Transformations in Convolutional Neural Networks

Michele Alberti, Angela Botros, Schuetz Narayan, Rolf Ingold, Marcus Liwicki, Mathias Seuret

Auto-TLDR; Trainable and Spectrally Initializable Matrix Transformations for Neural Networks

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In this work, we introduce a new architectural component to Neural Networks (NN), i.e., trainable and spectrally initializable matrix transformations on feature maps. While previous literature has already demonstrated the possibility of adding static spectral transformations as feature processors, our focus is on more general trainable transforms. We study the transforms in various architectural configurations on four datasets of different nature: from medical (ColorectalHist, HAM10000) and natural (Flowers) images to historical documents (CB55). With rigorous experiments that control for the number of parameters and randomness, we show that networks utilizing the introduced matrix transformations outperform vanilla neural networks. The observed accuracy increases appreciably across all datasets. In addition, we show that the benefit of spectral initialization leads to significantly faster convergence, as opposed to randomly initialized matrix transformations. The transformations are implemented as auto-differentiable PyTorch modules that can be incorporated into any neural network architecture. The entire code base is open-source.

Exploring the Ability of CNNs to Generalise to Previously Unseen Scales Over Wide Scale Ranges

Ylva Jansson, Tony Lindeberg

Auto-TLDR; A theoretical analysis of invariance and covariance properties of scale channel networks

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The ability to handle large scale variations is crucial for many real world visual tasks. A straightforward approach to handling scale in a deep neural network is to process multiple rescaled image copies in a set of scale channels (subnetworks). Scale invariance can then, in principle, be achieved by using weight sharing between the scale channels together with max or average pooling over the outputs from the scale channels. The ability of such scale channel networks to generalise to scales not present in the training set over significant scale ranges has, however, not previously been explored. We, therefore, present a theoretical analysis of invariance and covariance properties of scale channel networks and perform an experimental evaluation of the ability of different types of scale channel networks to generalise to previously unseen scales. We identify limitations of previous approaches and propose a new type of foveated scale channel architecture, where the scale channels process increasingly larger parts of the image with decreasing resolution. Our proposed FovMax and FovAvg networks perform almost identically over a scale range of 8 also when training on single scale training data and give improvements in the small sample regime.

Dimensionality Reduction for Data Visualization and Linear Classification, and the Trade-Off between Robustness and Classification Accuracy

Martin Becker, Jens Lippel, Thomas Zielke

Auto-TLDR; Robustness Assessment of Deep Autoencoder for Data Visualization using Scatter Plots

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This paper has three intertwined goals. The first is to introduce a new similarity measure for scatter plots. It uses Delaunay triangulations to compare two scatter plots regarding their relative positioning of clusters. The second is to apply this measure for the robustness assessment of a recent deep neural network (DNN) approach to dimensionality reduction (DR) for data visualization. It uses a nonlinear generalization of Fisher's linear discriminant analysis (LDA) as the encoder network of a deep autoencoder (DAE). The DAE's decoder network acts as a regularizer. The third goal is to look at different variants of the DNN: ones that promise robustness and ones that promise high classification accuracies. This is to study the trade-off between these two objectives -- our results support the recent claim that robustness may be at odds with accuracy; however, results that are balanced regarding both objectives are achievable. We see a restricted Boltzmann machine (RBM) pretraining and the DAE based regularization as important building blocks for achieving balanced results. As a means of assessing the robustness of DR methods, we propose a measure that is based on our similarity measure for scatter plots. The robustness measure comes with a superimposition view of Delaunay triangulations, which allows a fast comparison of results from multiple DR methods.

Total Estimation from RGB Video: On-Line Camera Self-Calibration, Non-Rigid Shape and Motion

Antonio Agudo

Auto-TLDR; Joint Auto-Calibration, Pose and 3D Reconstruction of a Non-rigid Object from an uncalibrated RGB Image Sequence

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In this paper we present a sequential approach to jointly retrieve camera auto-calibration, camera pose and the 3D reconstruction of a non-rigid object from an uncalibrated RGB image sequence, without assuming any prior information about the shape structure, nor the need for a calibration pattern, nor the use of training data at all. To this end, we propose a Bayesian filtering approach based on a sum-of-Gaussians filter composed of a bank of extended Kalman filters (EKF). For every EKF, we make use of dynamic models to estimate its state vector, which later will be Gaussianly combined to achieve a global solution. To deal with deformable objects, we incorporate a mechanical model solved by using the finite element method. Thanks to these ingredients, the resulting method is both efficient and robust to several artifacts such as missing and noisy observations as well as sudden camera motions, while being available for a wide variety of objects and materials, including isometric and elastic shape deformations. Experimental validation is proposed in real experiments, showing its strengths with respect to competing approaches.

Locality-Promoting Representation Learning

Johannes Schneider

Auto-TLDR; Locality-promoting Regularization for Neural Networks

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This work investigates questions related to learning features in convolutional neural networks (CNN). Empirical findings across multiple architectures such as VGG, ResNet, Inception and MobileNet indicate that weights near the center of a filter are larger than weights on the outside. Current regularization schemes violate this principle. Thus, we introduce Locality-promoting Regularization, which yields accuracy gains across multiple architectures and datasets. We also show theoretically that the empirical finding could be explained by maximizing feature cohesion under the assumption of spatial locality.

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.

Cost Volume Refinement for Depth Prediction

João L. Cardoso, Nuno Goncalves, Michael Wimmer

Auto-TLDR; Refining the Cost Volume for Depth Prediction from Light Field Cameras

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Light-field cameras are becoming more popular in the consumer market. Their data redundancy allows, in theory, to accurately refocus images after acquisition and to predict the depth of each point visible from the camera. Combined, these two features allow for the generation of full-focus images, which is impossible in traditional cameras. Multiple methods for depth prediction from light fields (or stereo) have been proposed over the years. A large subset of these methods relies on cost-volume estimates -- 3D objects where each layer represents a heuristic of whether each point in the image is at a certain distance from the camera. Generally, this volume is used to regress a disparity map, which is then refined for better results. In this paper, we argue that refining the cost volumes is superior to refining the disparity maps in order to further increase the accuracy of depth predictions. We propose a set of cost-volume refinement algorithms and show their effectiveness.

P2D: A Self-Supervised Method for Depth Estimation from Polarimetry

Marc Blanchon, Desire Sidibe, Olivier Morel, Ralph Seulin, Daniel Braun, Fabrice Meriaudeau

Auto-TLDR; Polarimetric Regularization for Monocular Depth Estimation

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Monocular depth estimation is a recurring subject in the ﬁeld of computer vision. Its ability to describe scenes via a depth map while reducing the constraints related to the formulation of perspective geometry tends to favor its use. However, despite the constant improvement of algorithms, most methods exploit only colorimetric information. Consequently, robustness to events to which the modality is not sensitive to, like specularity or transparency, is neglected. In response to this phenomenon, we propose using polarimetry as an input for a self-supervised monodepth network. Therefore, we propose exploiting polarization cues to encourage accurate reconstruction of scenes. Furthermore, we include a term of polarimetric regularization to state-of-the-art method to take speciﬁc advantage of the data. Our method is evaluated both qualitatively and quantitatively demonstrating that the contribution of this new information as well as an enhanced loss function improves depth estimation results, especially for specular areas.

Quantization in Relative Gradient Angle Domain for Building Polygon Estimation

Yuhao Chen, Yifan Wu, Linlin Xu, Alexander Wong

Auto-TLDR; Relative Gradient Angle Transform for Building Footprint Extraction from Remote Sensing Data

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Building footprint extraction in remote sensing data benefits many important applications, such as urban planning and population estimation. Recently, rapid development of Convolutional Neural Networks (CNNs) and open-sourced high resolution satellite building image datasets have pushed the performance boundary further for automated building extractions. However, CNN approaches often generate imprecise building morphologies including noisy edges and round corners. In this paper, we leverage the performance of CNNs, and propose a module that uses prior knowledge of building corners to create angular and concise building polygons from CNN segmentation outputs. We describe a new transform, Relative Gradient Angle Transform (RGA Transform) that converts object contours from time vs. space to time vs. angle. We propose a new shape descriptor, Boundary Orientation Relation Set (BORS), to describe angle relationship between edges in RGA domain, such as orthogonality and parallelism. Finally, we develop an energy minimization framework that makes use of the angle relationship in BORS to straighten edges and reconstruct sharp corners, and the resulting corners create a polygon. Experimental results demonstrate that our method refines CNN output from a rounded approximation to a more clear-cut angular shape of the building footprint.

Adaptive Sampling of Pareto Frontiers with Binary Constraints Using Regression and Classification

Raoul Heese, Michael Bortz

Auto-TLDR; Adaptive Optimization for Black-Box Multi-Objective Optimizing Problems with Binary Constraints

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We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a straightfoward way for regression models with a normal probability density. We benchmark our approach with an evolutionary algorithm on multiple test problems.

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.

Radar Image Reconstruction from Raw ADC Data Using Parametric Variational Autoencoder with Domain Adaptation

Michael Stephan, Thomas Stadelmayer, Avik Santra, Georg Fischer, Robert Weigel, Fabian Lurz

Auto-TLDR; Parametric Variational Autoencoder-based Human Target Detection and Localization for Frequency Modulated Continuous Wave Radar

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This paper presents a parametric variational autoencoder-based human target detection and localization framework working directly with the raw analog-to-digital converter data from the frequency modulated continuous wave radar. We propose a parametrically constrained variational autoencoder, with residual and skip connections, capable of generating the clustered and localized target detections on the range-angle image. Furthermore, to circumvent the problem of training the proposed neural network on all possible scenarios using real radar data, we propose domain adaptation strategies whereby we ﬁrst train the neural network using ray tracing based model data and then adapt the network to work on real sensor data. This strategy ensures better generalization and scalability of the proposed neural network even though it is trained with limited radar data. We demonstrate the superior detection and localization performance of our proposed solution compared to the conventional signal processing pipeline and earlier state-of-art deep U-Net architecture with range-doppler images as inputs.