Related papers: Reflection Invariant and Symmetry Detection
Regular object detection methods output rectangle bounding boxes, which are unable to accurately describe the actual object shapes. Instance segmentation methods output pixel-level labels, which are computationally expensive for real-time…
Symmetry detection is a fundamental problem in computer vision, and symmetries serve as powerful priors for downstream tasks. However, existing learning-based methods for detecting 3D symmetries from single images have been almost…
A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is…
We describe a method that uses total internal reflection at the water-air interface inside a large, transparent tank, to measure the interface's deflections. Using this configuration, we obtain an optical set-up where the liquid surface…
Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study…
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive…
The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…
Computer vision has long relied on two kinds of correspondences: pixel correspondences in images and 3D correspondences on object surfaces. Is there another kind, and if there is, what can they do for us? In this paper, we introduce…
Motion trajectory recognition is important for characterizing the moving property of an object. The speed and accuracy of trajectory recognition rely on a compact and discriminative feature representation, and the situations of varying…
Rotation-invariant recognition of shapes is a common challenge in computer vision. Recent approaches have significantly improved the accuracy of rotation-invariant recognition by encoding the rotational invariance of shapes as hand-crafted…
Detecting and analyzing directional structures in images is important in many applications since one-dimensional patterns often correspond to important features such as object contours or trajectories. Classifying a structure as directional…
Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…
Photometric Stereo methods seek to reconstruct the 3d shape of an object from motionless images obtained with varying illumination. Most existing methods solve a restricted problem where the physical reflectance model, such as Lambertian…
With the advancement of deepfake generation techniques, the importance of deepfake detection in protecting multimedia content integrity has become increasingly obvious. Recently, temporal inconsistency clues have been explored to improve…
It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a similar result holds for Euclidean space in any number of dimensions. The…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
The rotation robustness property has drawn much attention to point cloud analysis, whereas it still poses a critical challenge in 3D object detection. When subjected to arbitrary rotation, most existing detectors fail to produce expected…
Understanding mechanical properties of materials requires not only complete determination of the three-dimensional response at a local scale, but also knowledge of the mode or the mechanism by which deformation takes place. Probing…
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…
This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…