Neural Poisson Surface Reconstruction: Resolution-Agnostic Shape Reconstruction from Point Clouds

We introduce Neural Poisson Surface Reconstruction (nPSR), an architecture for shape reconstruction that addresses the challenge of recovering 3D shapes from points. Traditional deep neural networks face challenges with common 3D shape discretization techniques due to their computational complexity at higher resolutions. To overcome this, we leverage Fourier Neural Operators to solve the Poisson equation and reconstruct a mesh from oriented point cloud measurements. nPSR exhibits two main advantages: First, it enables efficient training on low-resolution data while achieving comparable performance at high-resolution evaluation, thanks to the resolution-agnostic nature of FNOs. This feature allows for one-shot super-resolution. Second, our method surpasses existing approaches in reconstruction quality while being differentiable and robust with respect to point sampling rates. Overall, the neural Poisson surface reconstruction not only improves upon the limitations of classical deep neural networks in shape reconstruction but also achieves superior results in terms of reconstruction quality, running time, and resolution agnosticism

Explaining Image Classifiers with Multiscale Directional Image Representation

Image classifiers are known to be difficult to interpret and therefore require explanation methods to understand their decisions. We present ShearletX, a novel mask explanation method for image classifiers based on the shearlet transform -- a multiscale directional image representation. Current mask explanation methods are regularized by smoothness constraints that protect against undesirable fine-grained explanation artifacts. However, the smoothness of a mask limits its ability to separate fine-detail patterns, that are relevant for the classifier, from nearby nuisance patterns, that do not affect the classifier. ShearletX solves this problem by avoiding smoothness regularization all together, replacing it by shearlet sparsity constraints. The resulting explanations consist of a few edges, textures, and smooth parts of the original image, that are the most relevant for the decision of the classifier. To support our method, we propose a mathematical definition for explanation artifacts and an information theoretic score to evaluate the quality of mask explanations. We demonstrate the superiority of ShearletX over previous mask based explanation methods using these new metrics, and present exemplary situations where separating fine-detail patterns allows explaining phenomena that were not explainable before

Learning Interpretable Queries for Explainable Image Classification with Information Pursuit

Information Pursuit (IP) is an explainable prediction algorithm that greedily selects a sequence of interpretable queries about the data in order of information gain, updating its posterior at each step based on observed query-answer pairs. The standard paradigm uses hand-crafted dictionaries of potential data queries curated by a domain expert or a large language model after a human prompt. However, in practice, hand-crafted dictionaries are limited by the expertise of the curator and the heuristics of prompt engineering. This paper introduces a novel approach: learning a dictionary of interpretable queries directly from the dataset. Our query dictionary learning problem is formulated as an optimization problem by augmenting IP's variational formulation with learnable dictionary parameters. To formulate learnable and interpretable queries, we leverage the latent space of large vision and language models like CLIP. To solve the optimization problem, we propose a new query dictionary learning algorithm inspired by classical sparse dictionary learning. Our experiments demonstrate that learned dictionaries significantly outperform hand-crafted dictionaries generated with large language models

Deep microlocal reconstruction for limited-angle tomography

We present a deep-learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging. The algorithm is based on a recently developed digital wavefront set extractor as well as the well-known microlocal canonical relation for the Radon transform. We use the wavefront set information about x-ray data to improve the reconstruction by requiring that the underlying neural networks simultaneously extract the correct ground truth wavefront set and ground truth image. As a necessary theoretical step, we identify the digital microlocal canonical relations for deep convolutional residual neural networks. We find strong numerical evidence for the effectiveness of this approach