Vitaly Kober

The Karhunen–Loève (KL) expansion decomposes a stochastic process into a set of orthogonal functions with random coefficients. The basic idea of the decomposition is to solve the Fredholm integral equation associated with the covariance kernel of the process. The KL expansion is a powerful mathematical tool used to represent stochastic processes in a compact and efficient way. It has wide applications in various fields including signal processing, image compression, and complex systems modeling. The KL expansion has high computational complexity, especially for large data sets, since there is no single unique transformation for all stochastic processes and there are no fast algorithms for computing eigenvalues and eigenfunctions. One way to solve this problem is to use parametric models for the covariance function. In this paper, an explicit analytical solution of the KL expansion for a parametric model of oscillating covariance function with a small number of parameters is proposed. This model approximates the covariance functions of real images very well. Computer simulation results using a real image are presented and discussed.

SPIE Digital Library Proceedings

SPIE Digital Library Proceedings

SPIE Digital Library Proceedings

SPIE Digital Library Proceedings

Discrete cosine and sine transforms closely approximate the Karhunen–Loeve transform for first-order Markov stationary signals with high and low correlation coefficients, respectively. Discrete sinusoidal transforms can be used in data compression, digital filtering, spectral analysis and pattern recognition. Short-time transforms based on discrete sinusoidal transforms are suitable for the adaptive processing and time–frequency analysis of quasi-stationary data. The generalized sliding discrete transform is a type of short-time transform, that is, a fixed-length windowed transform that slides over a signal with an arbitrary integer step. In this paper, eight fast algorithms for calculating various sliding sinusoidal transforms based on a generalized solution of a second-order linear nonhomogeneous difference equation and pruned discrete sine transforms are proposed. The performances of the algorithms in terms of computational complexity and execution time were compared with those of recursive sliding and fast discrete sinusoidal algorithms. The low complexity of the proposed algorithms resulted in significant time savings.

Point cloud collection forming a 3D scene typically uses information from multiple data scans. The common approach is to register the point cloud pairs consequentially using a variant of the iterative closest point (ICP) algorithm, but most versions of the ICP algorithm only work correctly for a small movement between two point clouds. This makes it difficult to accumulate multiple scans. Global registration algorithms are also known, which theoretically process point clouds at arbitrary initial positions. Recently, a multiparameter variational functional was described and used in the ICP variant to register point clouds at arbitrary initial positions. The disadvantage of this algorithm was the need for manual selection of parameters. In this paper, a modified version of the algorithm with automatic selection of the model parameters is proposed. The proposed algorithm is a fusion of the ICP and RANSAC concepts. Moreover, the algorithm can be parallelized. The performance of the proposed algorithm is compared with that of known global registration algorithms.

A stereo matching method based on adaptive morphological correlation is presented. The point correspondences of an input pair of stereo images are determined by matching locally adaptive image windows using the suggested morphological correlation that is optimal with respect to an introduced binary dissimilarity-to-matching ratio criterion. The proposed method is capable of determining the point correspondences in homogeneous image regions and at the edges of scene objects of input stereo images with high accuracy. Furthermore, unknown correspondences of occluded and not matched points in the scene can be successfully recovered using a simple proposed post-processing. The performance of the proposed method is exhaustively tested for stereo matching in terms of objective measures using known database images. In addition, the obtained results are discussed and compared with those of two similar state-of-the-art methods.