Showing papers on "Kernel (image processing) published in 1985"

Fast numerical solution of nonlinear volterra convolution equations

Abstract: Numerical methods for general Volterra integral equations of the second kind need $O(n^2 )$ kernel evaluations and $O(n^2 )$ additions and multiplications. Here it is shown how the effort can be reduced for nonlinear convolution equations. Exploiting the convolution structure, most numerical methods need only $O(n)$ kernel evaluations. With the use of Fast Fourier Transform techniques only $O(n(\log n)^2 )$ additions and multiplications are necessary. The paper closes with numerical examples and comparisons.

Convolution with separable masks for early image processing

Abstract: Computational techniques for implementing the Marr-Hildreth edge detection operator, −∇2G(r) and its space-time extensions are considered. It is shown how this kind of convolution operation may be carried out simply and efficiently by factorizing the mask and performing the multidimensional convolution as a sequence of one-dimensional convolutions. For ad-dimensional mask of sizen, the computational effort required in order to carry out the sequence of 1D convolutions varies roughly asd2n compared tond for a multidimensional convolution. Computational examples carried out on a SIMD machine (an ICL Distributed Array Processor—DAP) are described and it is shown that convolution with masks of radius 8 on 64 × 64 images can be carried out in 13 ms in two dimensions (mask support ≈ 200 pixels) and 21 ms in three dimensions (support ≈ 2000 pixels). A brief comparison is made with the FFT technique for performing the convolution.

Fredholm theory of Wiener-Hopf equations in terms of realization of their symbols

Abstract: The Fredholm properties (index, kernel, image, etc) of Wiener-Hopf integral operators are described in terms of realization of the symbol for a class of matrix symbols that are analytic on the real line but not at infinity The realizations are given in terms of exponentially dichotomous operators The results obtained give a complete analogue of the earlier results for rational symbols

A note on duhamel integrals and running average filters

Abstract: The use of the principle of inclusion and exclusion is proved in computing the convolution of an image with a nonrectangular, spatially varying binary-valued point spread function. This proof is based on properties of convolution and superposition integrals.

Modifications of some first kind integral equations with logarithmic kernel to improve numerical conditioning

Abstract: We consider a pair of integral equations derived by Symm (1967) and Hsiao & MacCamy (1973) for use in various boundary value problems. We investigate the matrix which results when some collocation methods are applied to these equations. We find that thel2-condition number of the matrix can be reduced by performing three minor modifications of the integral equations.

Segmentation of three dimensional images

Abstract: In this paper, we describe the fundamental differences between three-dimensional (range) images and two-dimensional (luminance) images. A number of problems arise which are unique to range data, including in particular a strong sensitivity to quantization effects. Although range images and luminance images are both arrays of scalars, the range image conceptually represents a surface in space and cannot be naively manipulated using the conventional image processing functions such as 3 × 3 convolution kernels. If the range data are regarded as a sampling of a surface parametrized by the focal plane coordinates, it is possible to find a representation for the surface normal and for the surface curvature in terms of familiar-looking convolution kernels.

Video forming device using aperture synthesizing method

Abstract: PURPOSE:To speed up the processing of the aperture synthesizing by using kernel data having the number of bits less than that of a hologram data. CONSTITUTION:A phase detector 5 detects a phase by multiplying an ultrasonic echo signal or the like by a sine wave of which resonance frequency coincides with that of a vibrator from a scan controller 3 to form cosine and sine hologram signals. These signals are converted by A/D converters 6, 7 respectively and digital cosine and sine holograms are stored in buffers 8, 9 respectively. The contents of the buffers 8, 9 are read into a computer 10, convolution operation is executed by the kernel data having the number of bits less than that of the hologram data from the buit-in ROM and ultrasonic wave reflecting point image information is formed and displayed on a CRT monitor 14. Thus, the processing is simplified and speeded up and a reconstituted image in an area for video formation is formed simply and rapidly by the operation of aperture synthesizing using the kernel data having the small number of bits.

A characterization in the space of convolution operators

Abstract: We give a characterization of C°° elements in the space of convolution operators 0'., which belong to the Schwartz space if.

Two-dimensional convolution using number theoretic transforms without matrix transposition and without overlap

Abstract: The necessity of sectioning a large picture to compute a 2 dimensional convolution has many drawbacks, one of which is the size of the optimal sections. Starting from this consideration, it is shown that, if the input image array is a 22u × 22u matrix, the convolution can be computed efficiently using a small length Fermat number transform and, if enough fast memory space is provided, without transposing the matrix or overlap sectioning the input array. The paper investigates the case of pictures represented by approximately 1000 × 1000 pixels.