The fundamentals of average local variance--Part I: Detecting regular patterns

The method of average local variance (ALV) computes the mean of the standard deviation values derived for a 3 x 3 moving window on a successively coarsened image to produce a function of ALV versus spatial resolution. In developing ALV, the authors used approximately a doubling of the pixel size at each coarsening of the image. They hypothesized that ALV is low when the pixel size is smaller than the size of scene objects because the pixels on the object will have similar response values. When the pixel and objects are of similar size, they will tend to vary in response and the ALV values will increase. As the size of pixels increase further, more objects will be contained in a single pixel and ALV will decrease. The authors showed that various cover types produced single peak ALV functions that inexplicitly peaked when the pixel size was 1/2 to 3/4 of the object size. This paper reports on work done to explore the characteristics of the various forms of the ALV function and to understand the location of the peaks that occur in this function. The work was conducted using synthetically generated image data. The investigation showed that the hypothesis originally proposed in is not adequate. A new hypothesis is proposed that the ALV function has peak locations that are related to the geometric size of pattern structures in the scene. These structures are not always the same as scene objects. Only in cases where the size of and separation between scene objects are equal does the ALV function detect the size of the objects. In situations where the distance between scene objects are larger than their size, the ALV function has a peak at the object separation, not at the object size. This work has also shown that multiple object structures of different sizes and distances in the image provide multiple peaks in the ALV function and that some of these structures are not implicitly recognized as such from our perspective. However, the magnitude of these peaks depends on the response mix in the structures, complicating their interpretation and analysis. The analysis of the ALV Function is, thus, more complex than that generally reported in the literature.