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Current successful approaches for generic (non-semantic) segmentation rely mostly on edge detection and have leveraged the strengths of deep learning mainly by improving the edge detection stage in the algorithmic pipeline. This is in…
We study the expressivity of ReLU neural networks in the setting of a binary classification problem from a topological perspective. Recently, empirical studies showed that neural networks operate by changing topology, transforming a…
In a neural network with ReLU activations, the number of piecewise linear regions in the output can grow exponentially with depth. However, this is highly unlikely to happen when the initial parameters are sampled randomly, which therefore…
Although neural networks (NNs) with ReLU activation functions have found success in a wide range of applications, their adoption in risk-sensitive settings has been limited by the concerns on robustness and interpretability. Previous works…
Edge detection remains a fundamental yet challenging task in computer vision, especially under varying illumination, noise, and complex scene conditions. This paper introduces a Hybrid Multi-Stage Learning Framework that integrates…
Edge detection, a basic task in the field of computer vision, is an important preprocessing operation for the recognition and understanding of a visual scene. In conventional models, the edge image generated is ambiguous, and the edge lines…
Blur detection is the separation of blurred and clear regions of an image, which is an important and challenging task in computer vision. In this work, we regard blur detection as an image segmentation problem. Inspired by the success of…
We present an approach to leaf level segmentation of images of Arabidopsis thaliana plants based upon detected edges. We introduce a novel approach to edge classification, which forms an important part of a method to both count the leaves…
We show how neural models can be used to realize piece-wise constant functions such as decision trees. The proposed architecture, which we call locally constant networks, builds on ReLU networks that are piece-wise linear and hence their…
In recent years novel activation functions have been proposed to improve the performance of neural networks, and they show superior performance compared to the ReLU counterpart. However, there are environments, where the availability of…
Deep ReLU Networks can be decomposed into a collection of linear models, each defined in a region of a partition of the input space. This paper provides three results extending this theory. First, we extend this linear decompositions to…
We present a framework to derive upper bounds on the number of regions that feed-forward neural networks with ReLU activation functions are affine linear on. It is based on an inductive analysis that keeps track of the number of such…
Existing supervised approaches didn't make use of the low-level features which are actually effective to this task. And another deficiency is that they didn't consider the relation between pixels, which means effective features are not…
Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…
The morphological attributes of retinal vessels, such as length, width, tortuosity and branching pattern and angles, play an important role in diagnosis, screening, treatment, and evaluation of various cardiovascular and ophthalmologic…
An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually…
When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local…
We show that every piecewise linear function $f:R^d \to R$ with compact support a polyhedron $P$ has a representation as a sum of so-called `simplex functions'. Such representations arise from degree 1 triangulations of the relative…
Recently, convolutional neural networks (CNNs) have been used as a powerful tool to solve many problems of machine learning and computer vision. In this paper, we aim to provide insight on the property of convolutional neural networks, as…
Image deblurring is a fundamental and challenging low-level vision problem. Previous vision research indicates that edge structure in natural scenes is one of the most important factors to estimate the abilities of human visual perception.…