Abstract
The NP-Completeness theory states that exact and efficient algorithms are unlikely to exist for the class of NP-difficult problems. One way to deal with NP hardness is to relax the optimality requirement and look for solutions instead that are close to the optimum. This is the main idea behind the approximation algorithms, which are called heuristic or metaheuristic. The problem of motion estimation is a process with a high degree of computational complexity, it requires sufficient memory space and execution time. It represents the cost of static, dynamic and video image sequence coding. The main task is to minimize the distortion rate and improve visual quality. This makes research in the field of coding, image compression and video focus on finding efficient algorithms to carry out the estimation of movement in a reasonable time. If a list of images of n elements is analyzed, there are feasible solutions. So, an exhaustive search is too slow, even for small values of the solution space. Therefore, from a practical point of view, it is crucial to have efficient and fast heuristic algorithms that avoid thorough search. In this investigation we design and implement heuristic algorithms, based on the frequency domain, which are applied on the coefficients of the discrete transform of the cosine and wavelets. Also, we propose temporal domain algorithms such as block-matching algorithms, which focus your search on the maximum coincidence of the current image with the reference one. The algorithms used during the implementation of this research work were written with the mathematical programming language MATLAB. In addition, we review the basic concepts of image processing, video, compression algorithms and motion estimation frequently used. The evaluation of the algorithms was carried out with a set of images provided by a previous acquisition system. We show the improvement of visual quality, the amount of compressed or reconstructed information and the behavior of the methods in the search for similarities between pixels or images. Finally, we contribute to the dissemination of new lines of scientific research that lead to the expansion and improvement of the study, the generation of new knowledge, since it is a young area within the Education discipline of Nicaragua.
Highlights
Combinatorial Optimization is a branch of Optimization theory in applied mathematics and Computer Science, which is closely associated with Operations Research or Mathematical Programming, algorithm theory and computational complexity
For the implementation of the algorithms there are two alternatives, the first is to start from the theory, from the mathematical bases and program them in their entirety; the second option is to use some of the libraries or specific functions of Matlab software, since the mathematical development as we could see throughout the previous chapters is very extensive and the coding in software programs would take us a long time, necessary to be able to achieve the objectives of the thesis
In the case that a color image is used and needed in its gray levels, the Matlab function rgb2gray( ) will be used. To this input matrix, which being gray levels will be twodimensional, the Discrete Cosine Transform (DCT)-2D will be calculated using the dct2( ) function, its coefficients will be graphically represented by the mesh( ) function to measure performance when it is not achieved Appreciate the visual quality
Summary
Combinatorial Optimization is a branch of Optimization theory in applied mathematics and Computer Science, which is closely associated with Operations Research or Mathematical Programming, algorithm theory and computational complexity. Always in the search for Applied and Computational Mathematics 2020; 9(3): 85-95 better solutions in the space of solutions and good quality, research in this field in recent years has focused its attention on the design of general purpose techniques to guide the construction of solutions from different heuristics. These techniques are called metaheuristics and they are strategies to design and / or improve heuristic procedures aimed at obtaining high performance in solving problems that are difficult to solve. The term metaheuristic was introduced in [12] by Glover, and since many proposals have appeared for the design of better procedures to solve combinatorial problems
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