Fast and precise object search in a real scene image by representing the pattern by a function

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The aim of this research was to develop a fast and precise object search algorithm in a real scene image. In order to achieve a fast search, a method far representing an image by a polynomial and an algorithm for fast search using the Polynomial were developed.First, methods for representing an image by a function were investigated, and it was clarified that a polynomial was the best solution for the purpose of this research Since using standard least square method for approximating the image by a polynomial would cause the error, a method for approximating an image by a polynomial using the orthogonal polynomial was developed.Next, an algorithm for calculating the similarity between an image and the image represented by a polynomial effectively was developed. The similarity is calculated for each coefficient of the polynomial and the calculated similarities are summarized. Experimental results clarified that the developed method was much faster than the traditional methods. In addition, the developed algorithm was extended to calculate the inner product of an image and the basis which was necessary for using the subspace method. Using the subspace method, not only the recognition accuracy improves but also the error by the approximation decreases.Moreover, the idea of the developed method was applied for fast calculation of the continuous wavelet transform which was one of the important techniques in the field of signal processing. The integral calculation which is necessary for the continuous wavelet transform can be calculated very fast by the developed method.