Leonard A. Ferrari

Minimal rectangular partitions of digitized blobs

Abstract An algorithm is presented for partitioning a finite region of the digital plane into a minimum number of rectangular regions. It is demonstrated that the partition problem is equivalent to finding the maximum number of independent vertices in a bipartite graph. The graphs matching properties are used to develop an algorithm that solves the independent vertex problem. The solution of this graph-theoretical problem leads to a solution of the partition problem.

Simple algorithms and architectures for B-spline interpolation

It is proved that the Toeplitz binary value matrix inversion associated with mth-order B-spline interpolation can be implemented using only 2(m+1) additions. Pipelined architectures are developed for real-time B-spline interpolation based on simple running average filters. It is shown that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can be implemented using B-splines with M+2 multiplies. With insignificant loss of performance, the coefficients at the knots of the truncated sinc function can be approximated using coefficients which are powers of two. The resulting implementation requires only M+4m+6 additions. It is believed that the truncated sinc function approximated by zero-order B-spline functions actually achieves the best visual performance. >

Attenuation estimation with the zero-crossing technique: Phantom studies☆

Global and local attenuation coefficient estimations were performed in a phantom using a pulse echo method based on the rate of decay of zero crossing density. Focussed and unfocussed 3.5 MHz transducers were used. It was found that good global estimates could be made with either transducer over a 2:1 range of attenuation coefficient. Local estimates exhibit large bias errors and a high degree of variability. This variability diminishes in the focal zone of the focussed transducer and in the far field of the unfocussed transducer.

In vivo acoustic attenuation in liver: correlations with blood tests and histology.

Results of in vivo attenuation measurements in the liver have been obtained in 26 normal controls and in 51 patients with chronic diffuse liver disease. A modified real-time sector scanner was used for narrow-band amplitude attenuation examination. In the control group (people without apparent liver disease), a statistically significant correlation was found between acoustic attenuation in liver and two blood tests reflecting liver function: serum albumin (n = 24, r = 0.67, p = 0.002) and prothrombin time (n = 23, r = 0.63, p = 0.019). There was a statistically significant positive correlation between attenuation and fat for all biopsied patients (n = 51, r = 0.32, p = 0.023) and for patients with minimal fibrosis (n = 25, r = 0.45, p = 0.027). Although no correlation with fibrosis was found for all patients, in the group of patients with minimal fat there was a correlation with portal fibrosis (n = 33, r = 0.37, p = 0.035). This double blind prospective study shows that in the liver: (1) attenuation estimates appear correlated with clinical parameters (blood tests) in normal volunteers, and (2) large changes in fat affect narrow-band acoustic attenuation estimates to a greater degree than severe portal fibrosis in patients with chronic diffuse liver disease. Further research is needed before these estimates can become a clinical tool.

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 Duhamels theorem. A computer architecture for B-spline image filters is proposed and a complexity analysis and comparison to other approaches is provided.

A fast recursive algorithm for binary-valued two-dimensional filters

Abstract An efficient algorithm for computing the response of a linear spatially varying digital image filter to an arbitrary digital input image is described. This response is the superposition summation of the input image with a digital point spread function (PSF). It is assumed here that the PSF is binary valued. The approach to this computation is based on the Principle of Inclusion and Exclusion. This approach leads to a new efficient algorithm. This algorithm is also efficient when the PSF is spatially invariant.

Efficient two-dimensional filters using B -spline functions

This paper discusses the use of B -spline functions in efficient, approximate implementations of spatially varying and spatially invariant image filters. The methods are extensions of techniques used in numerical integration. The concept of Duhamel integrals is extended to the spatially varying case and when combined with the B -spline approximation leads to efficient algorithms which are more efficient that the direct computation or FFT approaches to 2-dimensional filtering.

Acoustical Imaging Using the Phase of Echo Waveforms

All conventional ultrasound imaging equipment, including static B-scanners and real time units, apply some form of envelope detection to the received radio-frequency (rF) signal in order to produce an image. Unfortunately, the envelope detection process essentially destroys all phase and spectral information which is readily available on each rF A-line waveform. Since such additional data offer a new dimension of information which has proven to be useful if not necessary, for quantitative tissue characterization, it is worthwhile to consider techniques for incorporating both phase and spectral information into an image. Here we propose one method for utilizing phase information in a fundamental way which produces a new class of ultrasound images. In brief, envelope detection is replaced by a frequency demodulation process to produce a signal with phase rather than amplitude information. This signal is fed to a standard digital scan converter, with appropriate storage algorithms, to produce an image. These phase or FM images have a totally different appearance from conventional amplitude or AM images. In-vivo scans of human subjects and various gray scale test objects show recognizable anatomical features (which overlay precisely with amplitude images) but significantly different texture and structural patterns.

Discrete splines and spline filters

An equation is derived for the Z transform of discrete polynomial splines for the general case of nonuniform knots. Two filter structures are provided for the computation and analysis of discrete splines, one for the one-sided factorial function representation and one for the B-spline representation. The filter inputs are the coefficient sequence and the corresponding knot set and the outputs are the discrete spline and its differences. The filter structures supply the input-output relations that can be used to analyze the effects of different patterns of knot nonuniformities given the coefficients, or vice versa. Digital filters with discrete spline unit-sample responses are analyzed. It is shown that filtering with a discrete spline filter can be implemented in two stages: the first stage is an MA filter with as many nodes as there are knots. and the second stage is an AR filter which performs successive summations. Because only the first stage involves multiplications, filters with large ratios of (length of unit-sample response) to (number of knots) can be implemented very efficiently. >

An efficient spline basis for multi-dimensional applications: image interpolation

In this paper, we present a new spline basis function, the 2-5-2 spline which can be computed using simple fixed point shifts and adds. We compare the results of 2-5-2 spline image interpolation with the results using the most commonly used spline basis, the B-spline. We also present efficient computational algorithms for the new spline basis function.