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.>

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.>

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.

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.

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.

Algorithms are described for the basic arithmetic operations and square rooting in a negative base. A new operation called polarization that reverses the sign of a number facilitates subtraction, using addition. Some special features of the negative-base arithmetic are also mentioned.

Described here is a deterministic division algorithm in a negative-base number system; here, the divisor is mapped into a suitable range by premultiplication, so that the choice of the quotient digit is deterministic.

Properties and construction of a class of test matrices, called " simply invertible matrices," are given.