# Art (Artiom) Kovnatsky Home   |   Research

I am interested in application of mathematics (optimization, statistics, probability, calculus of variations, differential equations, etc.) to real life problems.

# Publications

[PDF] [BibTeX]

[PDF] [BibTeX]

[PDF] [BibTeX]

## Laplacian colormaps: a framework for structure-preserving color transformations

### D. Eynard, A. Kovnatsky, M. M. Bronstein

#### Computer Graphics Forum (EUROGRAPHICS), 2014.

##### Mappings between color spaces are ubiquitous in image processing problems such as gamut mapping, decolorization, and image optimization for color-blind people. Simple color transformations often result in information loss and ambiguities (for example, when mapping from RGB to grayscale), and one wishes to find an image-specific transformation that would preserve as much as possible the structure of the original image in the target color space. In this paper, we propose Laplacian colormaps, a generic framework for structure-preserving color transformations between images. We use the image Laplacian to capture the structural information, and show that if the color transformation between two images preserves the structure, the respective Laplacians have similar eigenvectors, or in other words, are approximately jointly diagonalizable. Employing the relation between joint diagonalizability and commutativity of matrices, we use Laplacians commutativity as a criterion of color mapping quality and minimize it w.r.t. the parameters of a color transformation to achieve optimal structure preservation. We show numerous applications of our approach, including color-to-gray conversion, gamut mapping, multispectral image fusion, and image optimization for color deficient viewers.
[PDF] [BibTeX] [Code]

## Multimodal manifold analysis using simultaneous diagonalization of Laplacians

### D. Eynard, A. Kovnatsky, M. M. Bronstein, K. Glashoff, A. M. Bronstein

#### Multimodal manifold analysis using simultaneous diagonalization of Laplacians", IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI), 2015.

##### We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, retrieval, and clustering demonstrating that the joint spectral geometry frequently better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches to multimodal manifold analysis to our framework, of which the can be seen as particular cases.
[PDF] [BibTeX] [Code]

## Coupled quasi-harmonic bases

### A. Kovnatsky, M. M. Bronstein, A. M. Bronstein, K. Glashoff, R. Kimmel

#### Computer Graphics Forum (EUROGRAPHICS), 2013.

##### The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However, many applications involving multiple shapes are obstacled by the fact that Laplacian eigenbases computed independently on different shapes are often incompatible with each other. In this paper, we propose the construction of common approximate eigenbases for multiple shapes using approximate joint diagonalization algorithms. We illustrate the benefits of the proposed approach on tasks from shape editing, pose transfer, correspondence, and similarity. Dataset consistes of non- and isometrical shapes with pointwise ground-truth correspondences (assigned manually).
[PDF] [BibTeX] [Code] [Dataset]

[PDF] [BibTeX]

[PDF] [BibTeX]

[PDF] [BibTeX]

[PDF] [BibTeX]

[PDF] [BibTeX]

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