For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database

We present a method to infer a dense depth map from a color image and associated sparse depth measurements. Our main contribution lies in the design of an annealing process for determining co-visibility (occlusions, disocclusions) and the degree of regularization to impose on the model. We show that regularization and co-visibility are related via the fitness (residual) of model to data and both can be unified into a single framework to improve the learning process. Our method is an adaptive weighting scheme that guides optimization by measuring the residual at each pixel location over each training step for (i) estimating a soft visibility mask and (ii) determining the amount of regularization. We demonstrate the effectiveness our method by applying it to several recent unsupervised depth completion methods and improving their performance on public benchmark datasets, without incurring additional trainable parameters or increase in inference time.

This paper presents a novel method for the segmentation of regions of interest in mammograms. The algorithm concurrently delineates the boundaries of the breast boundary, the pectoral muscle, as well as dense regions that include candidate masses. The resulting representation constitutes an analysis of the global structure of the object in the mammogram. We propose a topographic representation called the isocontour map, in which a salient region forms a dense quasi-concentric pattern of contours. The topological and geometrical structure of the image is analyzed using an inclusion tree that is a hierarchical representation of the enclosure relationships between contours. The ¿saliency¿ of a region is measured topologically as the minimum nesting depth. Features at various scales are analyzed in multiscale isocontour maps, and we demonstrate that the multiscale scheme provides an efficient way of achieving better delineations. Experimental results demonstrate that the proposed method has potential as the basis for a prompting system in mammogram mass detection.

Deep neural networks (DNNs) have achieved great success in the last decades. DNN is optimized using the stochastic gradient descent (SGD) with learning rate annealing that overtakes the adaptive methods in many tasks. However, there is no common choice regarding the scheduled-annealing for SGD. This paper aims to present empirical analysis of learning rate annealing based on the experimental results using the major data-sets on the image classification that is one of the key applications of the DNNs. Our experiment involves recent deep neural network models in combination with a variety of learning rate annealing methods. We also propose an annealing combining the sigmoid function with warmup that is shown to overtake both the adaptive methods and the other existing schedules in accuracy in most cases with DNNs.

Regularization in the optimization of deep neural networks is often critical to avoid undesirable over-fitting leading to better generalization of model. One of the most popular regularization algorithms is to impose L2 penalty on the model parameters resulting in the decay of parameters, called weight-decay, and the decay rate is generally constant to all the model parameters in the course of optimization. In contrast to the previous approach based on the constant rate of weight-decay, we propose to consider the residual that measures dissimilarity between the current state of model and observations in the determination of the weight-decay for each parameter in an adaptive way, called adaptive weight-decay (AdaDecay) where the gradient norms are normalized within each layer and the degree of regularization for each parameter is determined in proportional to the magnitude of its gradient using the sigmoid function. We empirically demonstrate the effectiveness of AdaDecay in comparison to the state-of-the-art optimization algorithms using popular benchmark datasets: MNIST, Fashion-MNIST, and CIFAR-10 with conventional neural network models ranging from shallow to deep. The quantitative evaluation of our proposed algorithm indicates that AdaDecay improves generalization leading to better accuracy across all the datasets and models.