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We consider the problem of registering (aligning) two images to sub-pixel accuracy by optimization of objective functions constructed from the images' intensity values. We show that some widely used interpolation methods can introduce multiple local optima in the energy of the interpolated image which, if not counter-balanced by other terms, can cause local optima in registration objective functions including the sum of squared differences, cross correlation, and mutual information. We discuss different solutions to address the problem based on high degree B-spline interpolation, low pass filtering the images, and stochastic integration. Numerical examples using synthetic and real signals and images are shown.

We have developed a multiscale algorithm for elastic (or molded) alignment of images. There is a wide array of medical applications of elastic (as opposed to strictly rigid) alignment: Subtraction of previous images from current ones to identify changes is perhaps the most obvious. We present preliminary results of this molding technique on a variety of images, and conclude with some closing remarks about this and future directions and goals of this work.

We have developed a multiscale algorithm for elastic registration of images. Rigid registration has many applications but it is often limited by distortions in the images. For example, different views of the same object produce distortions. Common examples of slightly different views producing a distortion can be found in medical imaging, such as matching a current mammogram or chest radiograph with one from a previous year, and in remote sensing, such as matching images taken from different satellite positions. We have developed two methods of elastic registration. Both are multiscale but one used an iterative minimization of the local error and the other uses a windowed correlation. We present preliminary results of the elastic registration method used on windowed correlations.

We present two applications of wavelet and related techniques to problems arising in medical imaging. Both make considerable use of the edge detection and classification properties of wavelet-type representations. First we describe simple and effective techniques for image denoising and contrast enhancement based on the multiscale edge representation of images. These techniques are sufficiently flexible to successfully address the varying requirements posed by several different medical imaging modalities in common use today. Experimental results are presented to illustrate the application of these techniques to various types of medical images. Next we describe adapted waveform encoding, a technique for magnetic resonance imaging. One advantage of this technique is that it can be used to efficiently encode edge features of the object being imaged. This has a particular diagnostic application in tracking heart wall thickness during the cardiac cycle, which we present along with some experimental results along this line. We also present an analysis of the signal-to-noise ratios of images formed with this technique, as this is a factor of paramount importance in MRI. The fact that wavelet schemes tend to concentrate energy near edge features makes the result rather different than that found in standard Fourier based approaches. We indicate an exciting potential application of our technique: reducing spectral leakage in phosphorus spectroscopy.

A new method of filtering MR images is presented that uses wavelet transforms instead of Fourier transforms. The new filtering method does not reduce the sharpness of edges. However, the new method does eliminate any small structures that are similar in size to the noise eliminated. There are many possible extensions of the filter.