Adaptive Application of Feature Detection Operators Based on Image Variance

It is well known that the strength of a feature in an image may depend on the scale at which the appropriate detection operator is applied. It is also the case that many features in images exist significantly over a limited range of scales, and, of particular interest here, that the most salient scale may vary spatially over the feature. Hence, when designing feature detection operators, it is necessary to consider the requirements for both the systematic development and adaptive application of such operators over scale- and image-domains. We present an overview to the design of scalable derivative edge detectors, based on the finite element method, that addresses the issues of method and scale-adaptability. The finite element approach allows us to formulate scalable image derivative operators that can be implemented using a combination of piecewise-polynomial and Gaussian basis functions. The general adaptive technique may be applied to a range of operators. Here we evaluate the approach using image gradient operators, and we present comparative qualitative and quantitative results for both first and second order derivative methods.