Multiscale and multiresolution analysis

In this chapter, we describe the Gaussian scale-space in the spatial and intensity parameters, and we discuss the scale-selection algorithms for blob and edge detections. Image resolution is to some extent an artifact of the camera used, and with no prior knowledge, we seldomly can predict the size of objects in pixels in images. Thus, we must design algorithms that can adapt to a range of sizes. One such algorithm is to seek objects of fixed size and use this algorithm on a range of downsampled images. This is, however, not the most elegant method for this purpose, since the result depends on the initial offset of the origin of the camera grid and not the scened depicted. The Gaussian scale-space is a better structure in which to express multi-size or multi-scale algorithms. In the Gaussian scale-space, downsampling is replaced with convolution with a Gaussian kernel of width proportional to the downsampling factor. In the Gaussian scale-space, noise is gradually dampened, and images are infinitely smooth and differentiable, hence, mathematical differential descriptors can easily and robustly be adapted to discrete images in a multi-scale manner. Further, the Gaussian scale-space can also be applied to the intensity parameter, thus providing a well-posed notion of isophotes and smooth, differentiable histograms.