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Psychovisual models suggest human vision decouples low-level feature extraction from higher cognition by first forming intermediate abstractions. In contrast, deep learning-based vision models routinely extract and aggregate features using…
The topic of semantic segmentation has witnessed considerable progress due to the powerful features learned by convolutional neural networks (CNNs). The current leading approaches for semantic segmentation exploit shape information by…
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that…
Faithful yet compact explanations for vision models remain a challenge, as commonly used dense perturbation masks are often fragmented and overfitted, needing careful post-processing. Here, we present a training-free explanation method that…
An important capacity in visual object recognition is invariance to image-altering variables which leave the identity of objects unchanged, such as lighting, rotation, and scale. How do neural networks achieve this? Prior mechanistic…
Although there is no doubt that multi-parameter persistent homology is a useful tool to analyse multi-variate data, efficient ways to compute these modules are still lacking in the available topological data analysis toolboxes. Other issues…
Canonical principal parameters are introduced for surfaces in $\mathbb R^3$ without umbilical points. It is proved that in these parameters the surface is determined (up to position in space) by a pair of invariants satisfying a partial…
We first describe the numerical invariants attached to the second fundamental form of a spacelike surface in four-dimensional Minkowski space. We then study the configuration of the nu-principal curvature lines on a spacelike surface, when…
We propose a robust classification algorithm for curves in 2D and 3D, under the special and full groups of affine transformations. To each plane or spatial curve we assign a plane signature curve. Curves, equivalent under an affine…
Choosing the right representation for geometry is crucial for making 3D models compatible with existing applications. Focusing on piecewise-smooth man-made shapes, we propose a new representation that is usable in conventional CAD modeling…
Text-guided diffusion models have achieved remarkable success in object inpainting by providing high-level semantic guidance through text prompts. However, they often lack precise pixel-level spatial control, especially in scenarios…
It is known that humans display "shape bias" when classifying new items, i.e., they prefer to categorize objects based on their shape rather than color. Convolutional Neural Networks (CNNs) are also designed to take into account the spatial…
Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to…
An effective way to model the complex real world is to view the world as a composition of basic components of objects and transformations. Although humans through development understand the compositionality of the real world, it is…
Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based…
We study visual representation learning from a structural and topological perspective. We begin from a single hypothesis: that visual understanding presupposes a semantic language for vision, in which many perceptual observations correspond…
Unlike standard object classification, where the image to be classified contains one or multiple instances of the same object, indoor scene classification is quite different since the image consists of multiple distinct objects. Further,…
Face morphing is a problem in computer graphics with numerous artistic and forensic applications. It is challenging due to variations in pose, lighting, gender, and ethnicity. This task consists of a warping for feature alignment and a…
A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…