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Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…
An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element…
Image hashing is the process of associating a short vector of bits to an image. The resulting summaries are useful in many applications including image indexing, image authentication and pattern recognition. These hashes need to be…
We address the problem of decomposing a single image into reflectance and shading. The difficulty comes from the fact that the components of image---the surface albedo, the direct illumination, and the ambient illumination---are coupled…
Despite the growing use of transformer models in computer vision, a mechanistic understanding of these networks is still needed. This work introduces a method to reverse-engineer Vision Transformers trained to solve image classification…
Vision Transformers rely on fixed patch tokens that ignore the spatial and semantic structure of images. In this work, we introduce an end-to-end differentiable tokenizer that adapts to image content with pixel-level granularity while…
We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer perceptrons). When they achieve good results in classification, we…
Recent advances in implicit neural representations and differentiable rendering make it possible to simultaneously recover the geometry and materials of an object from multi-view RGB images captured under unknown static illumination.…
We present an efficient method for joint optimization of topology, materials and lighting from multi-view image observations. Unlike recent multi-view reconstruction approaches, which typically produce entangled 3D representations encoded…
Lighting prediction from a single image is becoming increasingly important in many vision and augmented reality (AR) applications in which shading and shadow consistency between virtual and real objects should be guaranteed. However, this…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
We present a technique for estimating the shape and reflectance of an object in terms of its surface normals and spatially-varying BRDF. We assume that multiple images of the object are obtained under fixed view-point and varying…
Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to…
We introduce a new network structure for decomposing an image into its intrinsic albedo and shading. We treat this as an image-to-image transformation problem and explore the scale space of the input and output. By expanding the output…
The study of derivations and their generalizations on non-associative algebras has proven to be fundamental in understanding the internal symmetries and algebraic dynamics of such structures. In this paper, we investigate derivations and…
Here the role and influence of aberrations in optical imaging systems employing partially coherent complex scalar fields is studied. Imaging systems require aberrations to yield contrast in the output image. For linear shift-invariant…
Segmenting salient objects in an image is an important vision task with ubiquitous applications. The problem becomes more challenging in the presence of a cluttered and textured background, low resolution and/or low contrast images. Even…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
Intrinsic Image Decomposition is an open problem of generating the constituents of an image. Generating reflectance and shading from a single image is a challenging task specifically when there is no ground truth. There is a lack of…
Image deblurring techniques play important roles in many image processing applications. As the blur varies spatially across the image plane, it calls for robust and effective methods to deal with the spatially-variant blur problem. In this…