Spectral and rank order approaches to texture analysis

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Abstract
There are two major approaches to texture analysis, both supported by physiological evidence: those based on the spatial statistics, and those based on its spectral properties. One of the most sophisticated spectral approaches to texture is that based on the Wigner distribution where the attributes computed for each pixel encapsulate both the local spectral and phase properties of the local Fourier transform in a unique real spectrum. On the other hand, some of the most efficient methods which operate in the spatial domain alone, are those based on rank order functions. Before one embarks on the use of the sophisticated methods, it is worth exploring the efficient ones to the limit of their performance. In this paper we investigate these two major approaches and compare their performance both in terms of quality of results and efficiency. The problem we consider is that of detecting defective blobs and cracks on complex textural backgrounds. We show that in most cases rank order approaches can perform well, although no unique method can be employed for both types of defects. On the other hand, the Wigner approach with a very small modification can cope with both types of defects and handle even the identification of very subtle cracks. Thus, it seems that for any real time performance inspection system, the rank order approaches should form the front end with the more sophisticated methods coming in play when necessary.