Browse Theses

This dissertation presents a new technique for representing digital pictures. The principal benefit of this representation is that it greatly simplifies the problem of finding the correspondence between components in the description of two pictures.

This representation technique is based on a new class of reversible transforms (the Difference of Low Pass or DOLP transform). A DOLP transform separates a signal into a set of band-pass components. The set of band-pass filters used in a DOLP transform are defined by subtracting adjacent members of a sequence of low-pass filters. This sequence of low-pass filters is formed by scaling a low-pass filter in size by an exponential set of scale factors. The result of these subtractions is a set of band-pass filters which are all scaled copies of a smallest band-pass filter.

Several techniques are presented for reducing the complexity of computing a DOLP transform. It is shown that as the each band-pass image can be resampled at a sample rate proportional to the scale of the band-pass image. This is called a Sampled DOLP transform. Resampling reduces the cost of computing a DOLP transform from O(N('2)) multiplies('1) to O(N Log N) multiplies and reduces the memory requirements from O(N Log N) storage elements to (DBLTURN) 3 N storage elements.

A fast algorithm for computing the DOLP transform is then presented. This algorithm, called "cascade convolution with expansion" is based on the auto-convolution scaling property of Gaussian functions. Cascaded convolution with expansion also reduces the cost of computing a DOLP transform to O(N Log N) multiplies. When combined with resampling, this fast algorithm can compute a Sampled DOLP transform in 3 X(,(CCIRC)) N multiplies.('2)

Techniques are then described for constructing a structural description of an image from its Sampled DOLP transform. The symbols in this description are detected by detecting local peaks and ridges in each band-pass image, and among all of the band-pass images. This description has the form of a tree of peaks, with the peaks interconnected by chains of symbols from the ridges. The tree of peaks has a structure which can be matched despite changes in size, orientation, or position of the gray scale shape that is described.

The tree of peaks permits the global shape of a gray-scale form^to be matched independently of the high resolution details of the^form. Thus it can be used for rapidly searching through a data base^of prototype descriptions for potential matches. This representation^is very efficient for finding the correspondence of components of^forms from two images. In such matching the peaks serves as the^tokens for which correspondence is determined. The^correspondence of peaks at each band-pass level constrain the^possible matches at the next, higher resolution image. This^representation can also be used to describe forms which are^textured or have blurry boundaries. Examples are presented in

which the descriptions of images of the same object are matched despite changes in the size and image plane orientation of the^object.

^^('1)N is the number of sample points in an image or signal.^('2)X(,(CCIRC)) is the number of coefficients in the smallest low-pass filter.