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

本研究的目的是在真实的场景图像中开发一种快速、精确的目标搜索算法。为了实现快速搜索，提出了用多项式表示图像的方法和用多项式进行快速搜索的算法.首先，研究了用函数表示图像的方法，并阐明了多项式是本研究的最佳解.由于用标准最小二乘法用多项式逼近图像会产生误差，提出了一种利用正交多项式对图像进行多项式逼近的方法，并提出了一种有效计算图像与多项式表示的图像之间相似度的算法。计算多项式的每个系数的相似性，并总结计算的相似性。实验结果表明，该方法比传统方法快得多。此外，该算法被扩展到计算内积的图像和基础，这是必要的使用子空间方法。该方法不仅提高了识别精度，而且减小了逼近误差，并将其思想应用于连续小波变换的快速计算，连续小波变换是信号处理领域的重要技术之一。连续小波变换所需的积分计算，可以非常快速地计算所开发的方法。

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.