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We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…

It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance $\epsilon>0$ and an $\epsilon$-irreducible algebraic affine plane curve $\mathcal C$ of…

In the field of spatial computing, one of the most essential tasks is the pose estimation of 3D objects. While rigid transformations of arbitrary 3D objects are relatively hard to detect due to varying environment introducing factors like…

Matching deformable objects using their shapes is an important problem in computer vision since shape is perhaps the most distinguishable characteristic of an object. The problem is difficult due to many factors such as intra-class…

When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…

Given a real algebraic curve, embedded in projective space, we study the computational problem of deciding whether there exists a hyperplane meeting the curve in real points only. More generally, given any divisor on such a curve, we may…

Image segmentation algorithms often depend on appearance models that characterize the distribution of pixel values in different image regions. We describe a new approach for estimating appearance models directly from an image, without…

Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…

A novel static algorithm is proposed for numerical reparametrization of periodic planar curves. The method identifies a monitor function of the arclength variable with the true curvature of an open planar curve and considers a simple…

This paper introduces a modular, non-deep learning method for filtering and refining sparse correspondences in image matching. Assuming that motion flow within the scene can be approximated by local homography transformations, matches are…

In this paper, we deal with the problem of optimizing a black-box smooth function over a full-dimensional smooth convex set. We study sets of feasible curves that allow to properly characterize stationarity of a solution and possibly carry…

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.

Recognizing precise geometrical configurations of groups of objects is a key capability of human spatial cognition, yet little studied in the deep learning literature so far. In particular, a fundamental problem is how a machine can learn…

We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets. The software package, called SetIntersectionProjection, is intended for the regularization of inverse…

We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…

Face recognition is a popular application of pat- tern recognition methods, and it faces challenging problems including illumination, expression, and pose. The most popular way is to learn the subspaces of the face images so that it could…

The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry. Point features, however, are not available…

Change detection is one of the most challenging issues when analyzing remotely sensed images. Comparing several multi-date images acquired through the same kind of sensor is the most common scenario. Conversely, designing robust, flexible…