Recursive algorithms for implementing digital image filters.

The B-spline functions are used to develop recursive algorithms for the efficient implementation of two-dimensional linear digital image filters. These filters may be spatially varying. The B-splines are used in a representation of the desired point spread function. We show that this leads to recursive algorithms and hardware implementations which are more efficient than either direct spatial domain filter realizations or FFT implementations. The Z-transform is used to develop a discrete version of Duhamel's theorem. A computer architecture for B-spline image filters is proposed and a complexity analysis and comparison to other approaches is provided.

Estimation of acoustic attenuation in liver using one megabyte of data and the zero-crossings technique.

Statistical fluctuations due to scatter-induced frequency variations in reflected acoustic pulses are a major problem when estimating acoustic attenuation. Disagreement exists in the ultrasound community as to how much data is sufficient to overcome these statistical fluctuations. The range of attenuation values for normal livers and a tissue equivalent phantom, using 1 megabyte of data per liver and the zero-crossings technique, was investigated. The significance of statistical fluctuations and their effects on attenuation are discussed.

The instantaneous frequency of a sinewave squelched bandlimited signal.

We study the instantaneous frequency of a signal which is formed by the summation of a sinewave and a bandlimited signal. We refer to the composite signal as a sinewave squelched or simply a squelched signal. We study the behavior of the squelched signal at its real zeros and extrema. In particular when the sinewave frequency is equal to the largest frequency in the signal's spectrum and its amplitude is greater than the signal's maximum amplitude, the analytic signal corresponding to this resultant signal (hereafter abbreviated as RZ signal) has only real zeros which contain all of the bandlimited signal's information. FM systems often use zero crossing techniques in the demodulation process. For a process with a normal amplitude distribution, we derive a relationship between the zero crossing density of an RZ converted signal and that of the original signal. One application of these analyses is in ultrasonic FM imaging. We give an explanation for the behavior of the FM imaging system as a function of amplitude and frequency of the added cosine.

Undersampling Errors in Region-of-Interest Tomography.

A detailed error analysis for the dual-sampling region-ofinterest X-ray tomography is presented. Simulation studies are used along with a range of sampling rates to quantitate the amount of sampling errors within the region of interest. It is shown that as the rate of sampling outside the region of interest becomes sparse the amount of sampling errors within the region of interest increases considerably.

A gestalt-guided heuristic boundary follower for x-ray images of lung nodules.

A ``piecewise heuristic'' follower of the boundaries of difficult-to-notice nonoverlapping blobs in digitized images is described. The technique was tested on 324 X-ray images of candidate lung nodules from eight radiographs with good results. This technique is several times faster than earlier detectors of the boundaries of lung nodules, while maintaining good fidelity of the detected boundaries.

Hierarchical representation of waveforms.

Ehrich and Foith have proposed an approach to the hierarchical representation of waveforms based on peak dominance relations. This correspondence proposes an alternative approach, derived from concepts of fuzzy connectedness. It also discusses the possibility of extending this approach to the description of curves and of images.