Related papers: A nonlinear elasticity model in computer vision
In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions…
We present an effective method for the matching of multimodal images. Accurate image matching is the basis of various applications, such as image registration and structure from motion. Conventional matching methods fail when handling noisy…
The use of image transformations is essential for efficient modeling and learning of visual data. But the class of relevant transformations is large: affine transformations, projective transformations, elastic deformations, ... the list…
We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…
A continuum mechanical theory incorporating an extension of Finsler geometry is formulated for fibrous soft solids. Especially if of biologic origin, such solids are nonlinear elastic with evolving microstructures. For example, elongated…
Image segmentation is an important task in the domain of computer vision and medical imaging. In natural and medical images, intensity inhomogeneity, i.e. the varying image intensity, occurs often and it poses considerable challenges for…
Subjective image quality metrics are usually evaluated according to the correlation with human opinion in databases with distortions that may appear in digital media. However, these oversee affine transformations which may represent better…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
This work presents a novel algorithm for transforming a neural network into a spline representation. Unlike previous work that required convex and piecewise-affine network operators to create a max-affine spline alternate form, this work…
Lossy image compression aims to represent images in as few bits as possible while maintaining fidelity to the original. Theoretical results indicate that optimizing distortion metrics such as PSNR or MS-SSIM necessarily leads to a…
Deformable Parts Models and Convolutional Networks each have achieved notable performance in object detection. Yet these two approaches find their strengths in complementary areas: DPMs are well-versed in object composition, modeling…
We introduce a new architecture called a conditional invertible neural network (cINN), and use it to address the task of diverse image-to-image translation for natural images. This is not easily possible with existing INN models due to some…
We propose here a proof of existence of a minimizer of a segmentation functional based on a priori information on target shapes, and formulated with level sets. The existence of a minimizer is very important, because it guarantees the…
This paper presents PointSSIM, a novel low-dimensional image-to-image comparison metric that is resolution invariant. Drawing inspiration from the structural similarity index measure and mathematical morphology, PointSSIM enables robust…
Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations…
Topology optimization (TO) can be viewed as seeking an optimal solution in the design space of a given TO problem. For weakly non-linear TO problems, e.g., compliance minimization, sensitivity-based methods typically converge well, whereas…
We present a framework for the multiscale modeling of finite strain magneto-elasticity based on physics-augmented neural networks (NNs). By using a set of problem specific invariants as input, an energy functional as the output and by…
We introduce a unified framework based on bi-level optimization schemes to deal with parameter learning in the context of image processing. The goal is to identify the optimal regularizer within a family depending on a parameter in a…
In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possible in modelling of molecular crystals, granular media, and…
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…