P. V. Sankar

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. >

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.

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.

Estimating the bandwidth of a normal process from the level crossings of its envelope

The zero crossing density of a band-limited normal process with a normal power spectrum can be used to determine the process rms frequency. In this correspondence, we give an algorithm for estimating the bandwidth of such a signal from the level crossing density of its envelope. We show that a band-limited normal process can be completely characterized using level crossings.

Curve and surface generation and refinement based on a high speed derivative algorithm

Abstract We propose an efficient algorithm for the refinement of curves and surfaces using simple knot B-splines. We develop a high speed algorithm for the computation of the r th derivative of an r th order spline and demonstrate that the inverse of this algorithm leads to an efficient refinement algorithm which is an order of magnitude faster than the well known Oslo algorithm. We show how the high speed derivative algorithm can also be used to directly generate spline curves and surfaces much more efficiently than linear combination algorithms and forward differencing.

Minimum complexity FIR filters and sparse systolic arrays

The properties of B-spline approximation and the integral/derivative properties of convolution lead to efficient algorithms for the implementation of multidimensional FIR filters. The implementations are of minimum time complexity under the Nyquist criterion. The algorithm can easily be implemented using a sparse systolic array architecture. The resulting B-spline convolvers have much lower circuit complexity than systolic architectures based on conventional convolution algorithms. A two-dimensional hardware implementation based on simplifications of current architectures is presented. >

Efficient algorithms for the implementation of general B-splines

Nonuniform B-splines are usually computed using the traditional recurrence relation Bi,r(u) = ui − uui+r−1−uiBi,r−1(u) + ui+r − uui+r − ui+1Bi+1,r−1(u).We derive a recurrence relation which relates the rth derivative of Bi,r(ū) to the (r − 1)th derivatives of Bi,r−1(u) and Bi + 1, r − 1u[formula]B(r)i, r(u) is comprised of r + 1 impulses (Dirac functions) at the knots [ūi, ūi + 1, . . . , ūi + r]. The amplitudes of the impulses are found from the recurrence. We show that equally spaced samples of the continuous B-spline function Bi, r(ū) can be computed exactly using recursive summation.

A unified approach to IFIR filter design using B-spline functions

An efficient procedure is presented for the design of interpolated finite impulse response (IFIR) filters with linear phase. The algorithm uses the uniform B-spline function as an interpolator and solves the optimal Chebyshev approximation problem on the appropriate subinterval. The technique can be used for the design of general low-pass, high-pass and bandpass filters. Although the number of multiplications of the IFIR filter is dependent on the bandwidth and the center frequency of the desired filter, this approach nearly always provides a substantial reduction in complexity when compared to other FIR and IFIR design procedures. >

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 signals spectrum and its amplitude is greater than the signals 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 signals 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.