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Alexander M. Bronstein
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Article
Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding
Many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space. The embedding process u...
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Article
Full and Partial Symmetries of Non-rigid Shapes
Symmetry and self-similarity are the cornerstone of Nature, exhibiting themselves through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence o...
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Chapter and Conference Paper
Spatially-Sensitive Affine-Invariant Image Descriptors
Invariant image descriptors play an important role in many computer vision and pattern recognition problems such as image search and retrieval. A dominant paradigm today is that of “bags of features”, a repres...
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Article
Partial Similarity of Objects, or How to Compare a Centaur to a Horse
Similarity is one of the most important abstract concepts in human perception of the world. In computer vision, numerous applications deal with comparing objects observed in a scene with some a priori known patte...
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Article
Topology-Invariant Similarity of Nonrigid Shapes
This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the obje...
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Book Series
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Book
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Article
Analysis of Two-Dimensional Non-Rigid Shapes
Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major pr...
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Chapter and Conference Paper
Regularized Partial Matching of Rigid Shapes
Matching of rigid shapes is an important problem in numerous applications across the boundary of computer vision, pattern recognition and computer graphics communities. A particularly challenging setting of th...
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Chapter
Topologically Constrained Isometric Embedding
Presented is an algorithm for nonlinear dimensionality reduction that uses both local(short) and global(long) distances in order to learn the intrinsic geometry of manifolds with complicated topology. Since ou...
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Chapter
Story of Cinderella
In this chapter, we address the question of what are the facial measures one could use in order to distinguish between people. Our starting point is the fact that the expressions of our face can, in most cases...
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Chapter and Conference Paper
Paretian Similarity for Partial Comparison of Non-rigid Objects
In this paper, we address the problem of partial comparison of non-rigid objects. We introduce a new class of set-valued distances, related to the concept of Pareto optimality in economics. Such distances allo...
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Chapter and Conference Paper
Matching Two-Dimensional Articulated Shapes Using Generalized Multidimensional Scaling
We present a theoretical and computational framework for matching of two-dimensional articulated shapes. Assuming that articulations can be modeled as near-isometries, we show an axiomatic construction of an a...
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Chapter and Conference Paper
On Separation of Semitransparent Dynamic Images from Static Background
Presented here is the problem of recovering a dynamic image superimposed on a static background. Such a problem is ill-posed and may arise e.g. in imaging through semireflective media, in separation of an illu...
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Chapter and Conference Paper
Robust Expression-Invariant Face Recognition from Partially Missing Data
Recent studies on three-dimensional face recognition proposed to model facial expressions as isometries of the facial surface. Based on this model, expression-invariant signatures of the face were constructed ...
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Chapter and Conference Paper
Facetoface: An Isometric Model for Facial Animation
A geometric framework for finding intrinsic correspondence between animated 3D faces is presented. We model facial expressions as isometries of the facial surface and find the correspondence between two faces ...
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Article
Three-Dimensional Face Recognition
An expression-invariant 3D face recognition approach is presented. Our basic assumption is that facial expressions can be modelled as isometries of the facial surface. This allows to construct expression-invar...
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Chapter and Conference Paper
Isometric Embedding of Facial Surfaces into \(\mathbb{S}^{\rm 3}\)
The problem of isometry-invariant representation and comparison of surfaces is of cardinal importance in pattern recognition applications dealing with deformable objects. Particularly, in three-dimensional fac...
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Chapter and Conference Paper
QML Blind Deconvolution: Asymptotic Analysis
Blind deconvolution is considered as a problem of quasi maximum likelihood (QML) estimation of the restoration kernel. Simple closed-form expressions for the asymptotic estimation error are derived. The asympt...
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Chapter and Conference Paper
Blind Deconvolution Using the Relative Newton Method
We propose a relative optimization framework for quasi maximum likelihood blind deconvolution and the relative Newton method as its particular instance. Special Hessian structure allows its fast approximate co...
