OVSJANIKOV , Maks

In this paper, we provide stability guarantees for two frameworks that are based on the notion of functional maps – the shape difference operators introduced in [?] and the framework of [?] which is used to analyze and visualize the deformations between shapes induced by a functional map. We consider two types of perturbations in our analysis:...

This paper presents a framework for object recognition using topological persistence. In particular, we show that the so-called persistence diagrams built from functions defined on the objects can serve as compact and informative descriptors for images and shapes. Complementary to the bag-of-features representation, which captures the...

We present an efficient and robust method for extracting curvature information, sharp features, and normal directions of a piecewise smooth surface from its point cloud sampling in a unified framework. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in...

In this article, we address the problem of devising signatures using the framework of persistent homology.Considering a compact length space with curvature bounded above, we build, either for every point or for the shape itself, a topological signature that is provably stable to perturbations of the space in the Gromov-Hausdorff distance. This...

Comparing points on 3D shapes is among the fundamental operations in shape analysis. To facilitate this task, a great number of local point signatures or descriptors have been proposed in the past decades. However, the vast majority of these descriptors concentrate on the local geometry of the shape around the point, and thus are insensitive to...

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics...

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics...

In this paper, we propose a novel pooling approach for shape classification and recognition using the bag-of-words pipeline, based on topological persistence, a recent tool from Topological Data Analysis. Our technique extends the standard max-pooling, which summarizes the distribution of a visual feature with a single number, thereby losing...

In this paper, we combine two ideas: persistence-based clustering and the Heat Kernel Signature (HKS) function to obtain a multi-scale isometry invariant mesh segmentation algorithm. The key advantages of this approach is that it is tunable through a few intuitive parameters and is stable under near-isometric deformations. Indeed the method...

A common operation in many geometry processing algorithms consists of finding correspondences between pairs of shapes by finding structure-preserving maps between them. A particularly useful case of such maps is isometries, which preserve geodesic distances between points on each shape. Although several algorithms have been proposed to find...

We introduce a novel method for non-rigid shape matching, designed to address the symmetric ambiguity problem present when matching shapes with intrinsic symmetries. Unlike the majority of existing methods which try to overcome this ambiguity by sampling a set of landmark correspondences, we address this problem directly by performing shape...

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry processing, their irregular and combinatorial structure often make them unsuitable for learning-based...

Vector fields on surfaces are fundamental in various applications in computer graphics and geometry processing. In many cases, in addition to representing vector fields, the need arises to compute their derivatives, for example, for solving partial differential equations on surfaces or for designing vector fields with prescribed smoothness...

In this paper, we introduce a novel coordinate-free method for manipulating and analyzing vector fields on discrete surfaces. Unlike the commonly used representations of a vector field as an assignment of vectors to the faces of the mesh, or as real values on edges, we argue that vector fields can also be naturally viewed as operators whose...

In this paper we propose a method for analyzing and visualizing individual maps between shapes, or collections of such maps. Our method is based on isolating and highlighting areas where the maps induce significant distortion of a given measure in a multi-scale way. Unlike the majority of prior work which focuses on discovering maps in the...

We develop a novel formulation for the notion of shape differences, aimed at providing detailed information about the location and nature of the differences or distortions between the two shapes being compared. Our difference operator, derived from a shape map, is much more informative than just a scalar global shape similarity score, rendering...

Notions of similarity and correspondence between geometric shapes and images arecentral to many tasks in geometry processing, computer vision, and computer graphics.The goal of this course is to familiarize the audience with a set of recent techniques thatgreatly facilitate the computation of mappings or correspondences between...