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In signal processing it is useful to simultaneously analyze the space and frequency characteristics of a signal. While the Fourier transform gives the frequency information of the signal, it is not localized. This means that we cannot determine which part of a (perhaps long) signal produced a particular frequency. It is possible to use a short time Fourier transform for this purpose, however the short time Fourier transform limits the basis functions to be sinusoidal. To provide a more flexible space-frequency signal decomposition several filters (including wavelets) have been proposed. The Log-Gabor〔D. J. Field. Relations between the statistics of natural images and the response properties of cortical cells. J. Opt. Soc. Am. A, 1987, pp. 2379-2394.〕 filter is one such filter that is an improvement upon the original Gabor filter.〔D. Gabor. Theory of communication. J. Inst. Electr. Eng. 93, 1946.〕 The advantage of this filter over the many alternatives is that it better fits the statistics of natural images compared with Gabor filters and other wavelet filters. ==Applications== The Log-Gabor filter is able to describe a signal in terms of the local frequency responses. Because this is a fundamental signal analysis technique, it has many applications in signal processing. Indeed, any application that uses Gabor filters, or other wavelet basis functions may benefit from the Log-Gabor filter. However, there may not be any benefit depending on the particulars of the design problem. Nevertheless, the Log-Gabor filter has been shown to be particularly useful in image processing applications, because it has been shown to better capture the statistics of natural images. In image processing, there are a few low-level examples of the use of Log-Gabor filters. Edge detection is one such primitive operation, where the edges of the image are labeled. Because edges appear in the frequency domain as high frequencies, it is natural to use a filter such as the Log-Gabor to pick out these edges.〔Z. Xiao, C. Guo, Y. Ming, and L. Qiang. Research on log Gabor wavelet and its application in image edge detection. In International Conference on Signal Processing volume 1, pages 592–595 Aug 2002.〕〔Sylvain Fischer, Filip Sroubek, Laurent U. Perrinet, Rafael Redondo, Gabriel Cristobal. Self-invertible 2D log-Gabor wavelets. Int. Journal of Computional Vision, 2007〕 These detected edges can be used as the input to a segmentation algorithm or a recognition algorithm. A related problem is corner detection. In corner detection the goal is to find points in the image that are corners. Corners are useful to find because they represent stable locations that can be used for image matching problems. The corner can be described in terms of localized frequency information by using a Log-Gabor filter.〔X. Gao, F. Sattar, and R. Venkateswarlu. Multiscale corner detection of gray level images based on log-Gabor wavelet transform. IEEE Transactions on Circuits and Systems for Video Technology, 17(7):868–875, July 2007.〕 In pattern recognition, the input image must be transformed into a feature representation that is easier for a classification algorithm to separate classes. Features formed from the response of Log-Gabor filters may form a good set of features for some applications because it can locally represent frequency information. For example, the filter has been successfully used in face expression classification.〔N. Rose. Facial expression classification using Gabor and log-Gabor filters. In International Conference on Automatic Face and Gesture Recognition (FGR), pages 346–350, April 2006.〕 There is some evidence that the human visual system processes visual information in a similar way.〔J. G. Daugman. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. Journal of the Optical Society of America, 1985, pp. 1160-9.〕 There are a host of other applications that require localized frequency information. The Log-Gabor filter has been used in applications such as image enhancement,〔W. Wang, J. Li, F. Huang, and H. Feng. Design and implementation of log-Gabor filter in fingerprint image enhancement. Pattern Recognition Letters, 2008. pp. 301–308.〕 speech analysis,〔L. He, M. Lech, N. Maddage, and N. Allen. Stress and emotion recognition using log-Gabor filter analysis of speech spectrograms. Affective Computing and Intelligent Interaction, 2009, pp. 1-6〕 contour detection,〔Sylvain Fischer, Rafael Redondo, Laurent Perrinet, Gabriel Cristobal. Sparse approximation of images inspired from the functional architecture of the primary visual areas. EURASIP Journal on Advances in Signal Processing, special issue on Image Perception, 2007〕 texture synthesis 〔Paula S. Leon, Ivo Vanzetta, Guillaume S. Masson, Laurent U. Perrinet. Motion Clouds: Model-based stimulus synthesis of natural-like random textures for the study of motion perception. Journal of Neurophysiology, 107(11):3217--3226, 2012〕 and image denoising 〔P. Kovesi. Phase preserving denoising of images. The Australian Pattern Recognition Society Conference: DICTA’99, 1999, pp. 212-217.〕 among others. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Log Gabor filter」の詳細全文を読む スポンサード リンク
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