Integrated Directional Derivative Gradient Operator

Abstract

Accurate edge direction information is required in many image processing applications. A variety of operators for computing local edge direction have been proposed, many of them estimating a kind of gradient. These operators face two major problems. One problem is the inherent bias in their estimate of edge direction. The bias itself is a function of edge direction. Another problem is their sensitivity to the presence of noise in the image data. The second problem can be alleviated by an increase in the processing neighborhood size but usually at the expense of an increase in estimate bias and also inefrors in the processing of small or thin objects. An operator based on the cubic facet model is discussed, which reduces sharply both estimate bias and noise sensitivity with no increase in computational complexity. The measure of gradient strength is the maximum value of the integral of the first directional derivative taken over a rectangular or square neighborhood, the maximum being taken over all possible directions for the directional derivative. The line direction which maximizes the integral defines the new estimate of gradient direction. Experimental results show the superiority of this operator to others such as the Roberts operator, the Prewitt operator, the Sobel operator, and the standard cubic facet gradient operator for step edges and ramp edges. Under zero-noise conditions the 7× 7 integrated directional derivative gradient operator has a worst bias of less than 0.