In this paper, the problem of head pose estimation is described. The solution consists of several stages. The clustering is a critical step. The clustering of feature points of the image is consuming and important step that needs to simplify and speed up. For this task, it is proposed to use the properties of a random walk on the graph. The random walk can lead to a measure of cluster cohesion. This approach is closely related to spectral graph theory. The paper presents formulas, steps of the algorithm and an example of calculations. Experiments and comparisons are made with the closest analogue, the method of normalized cut

We discuss the development of a structural descriptor for object detection in images. The descriptor is based on a graph, whose vertices are the centers of mass of segment features.  The embedding of the graph in a vector space is implemented using a Young-Householder decomposition and based on differential geometry. Compound curves are used to describe the relationship between the points. The image graph is described by a matrix of curvature parameters. The distance matrix for the graphs of the candidate object and the reference object is calculated using the Hausdorff metric. A multidimensional scaling method is used to represent the results. Images of test objects and images of human faces are used to study the developed approach. A comparison of the developed descriptor with the Viola-Jones method is performed when detecting a human head in the image. The advantage of the developed approach is the image rotational invariance in the plane while searching for objects. The descriptor can detect objects rotated in space by angles of up to 50 degrees. Using the mass centers of segments of features as the graph vertices makes the approach more robust to changes in image acquisition angles in comparison with the approach that uses image features as the graph vertices.

ABSTRACT:Recognition of human pose is an actual problem in computer vision. To increase the reliability of the recognition it is proposed to use structured information in the form of graphs. The spectrum of graphs is applied for the comparison of the structures. Image skeletonization is used to construct graphs. Line segments are the nodes of the graph. The end point of line segments are the edges of the graph. The angles between adjacent segments are used to set the weights of the adjacency matrix. The Laplacian matrix is used to generate the spectrum graph. The algorithm consists of the following steps. The graph on the basis of the vectorized image is constructed. The angles between the adjacent segments are calculated. The Laplacian matrix on the basis of the linear graph is calculated. The eigenvalues and eigenvectors of the Laplacian matrix are calculated. The spectral matrix is calculated using its eigenvalues and eigenvectors of the Laplacian matrix. The principal component method is used for the data representation in the space of smaller dimensions. The results of the algorithm are given.

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