A smile is a representative expression of happiness or high quality-of-life; however, automatic recognition of a smile according to happiness remains a challenging task. Because expressions of happiness are strongly dependent upon physical condition and occurrence of other emotions, and similar facial expression often occur under different emotions, we consider that there is no absolute visual pattern of a smile corresponding to happiness. Therefore, in this study, we assumed that a ``smile with happiness'' is observed as the temporal ascent in the degree of smiling and attempted to recognize this by capturing changes in facial expression within temporally sequential images. As an implementation of this scheme, we proposed a Siamese-structure deep neural network to compare facial expressions in two input images and estimate the existence of smile ascension or descension. For primal analysis of the proposed network, we developed a unique smiling dataset containing image pairs with various changes in smiling degree, including slight changes. The results demonstrated that the proposed method achieved nearly perfect recognition with >0.95 accuracy when recognizing changes in the degree of smiling that humans certainly recognize. Attention regions that contributed to the predicted labels were concentrated on the mouth, cheeks, and tail of the eyes, which indicates a reasonable function for recognizing changes in smiling degree was constructed by the proposed method.