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# Fast Image Gradient Direction Calculation - Algorithm and Circuit

IP.com Disclosure Number: IPCOM000060492D
Original Publication Date: 1986-Apr-01
Included in the Prior Art Database: 2005-Mar-08
Document File: 2 page(s) / 37K

IBM

Dom, BE: AUTHOR

## Abstract

An efficient algorithm and circuit are used to calculate the direction of the image gradient vector Af from a grey level image. The algorithm and circuit provide for the assignment of directions × of Af when working with angles after they have been quantized. The algorithm returns sector values 0 to 7, and is designed for use with integer greyscale values. In automatic image analysis and processing, the direction, ×, of the image gradient vector Af, where f(x,y) is a grey level image must be determined. This gradient direction can be calculated by using the inverse tangent function with differences between neighboring pixels as arguments (× = arctan (Wxf, Wyf)). The gradient direction is then quantized to one of eight 45-degree sectors centered about the eight cardinal directions.

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Fast Image Gradient Direction Calculation - Algorithm and Circuit

An efficient algorithm and circuit are used to calculate the direction of the image gradient vector Af from a grey level image. The algorithm and circuit provide for the assignment of directions × of Af when working with angles after they have been quantized. The algorithm returns sector values 0 to 7, and is designed for use with integer greyscale values. In automatic image analysis and processing, the direction, ×, of the image gradient vector Af, where f(x,y) is a grey level image must be determined. This gradient direction can be calculated by using the inverse tangent function with differences between neighboring pixels as arguments (× = arctan (Wxf, Wyf)). The gradient direction is then quantized to one of eight 45-degree sectors centered about the eight cardinal directions. However, a problem is introduced by having the sectors centered on the cardinal directions. The simple shifting operation to center the sectors on the cardinal directions works fine, when working with angles before they have been quantized, but after quantization, it is impossible to unambiguously assign directions from the uncentered to the centered sectors. The following algorithm performs the calculation in a fast, memory-efficient manner returning sector values 0 to 7. The algorithm is designed for use with integer greyscale values. For simplicity, assume they are 8-bit values [0,255]. In the description below, the sy...