A Progressive Approach to Feedback-Controlled Edge Detection Using Boolean Derivatives

Edge Detection is an important image processing operation with applications such as 3D reconstruction, recognition, image enhancement, image restoration and compression. Several edge detectors have been developed in the past decades. However, no single edge detector is best suited for all applications. An ideal edge detector would arrive at satisfactory edge maps for binary, grayscale or even multi-dimensional inputs across various applications and would have parameters that can be automatically selected without user intervention. Here, we survey existing edge detection techniques, introduce a new approach to edge detection and improvise the algorithm to produce better edge quality while keeping the system tunable. Binary edge detection using Boolean derivatives has been proven to be a fast and effective alternative to commonly used edge detectors. Our edge detection algorithm that also uses the Partial Derivative of Boolean Functions offers competitive and often better results or edge maps compared to several popular methods. The novelty of the approach is its applicability to binary and multi-bit (grayscale) data with no need for pre-filtering. We also present innovative ways to extend partial derivatives of Boolean functions to find edges in grayscale images. A new concept in edge detection that is better suited for application-specific image processing is introduced. The grayscale or multi-bit image is mapped to a set of several binary images. This is followed by the application of edge detection algorithms on these binary images and a fusion of the individual edge maps. A novel polynomial based binarization method is also presented. An evolutionary approach to the fusion of edgemaps renders the algorithm adaptive. Experimental results have shown that this new concept has several advantages. It produces edges of better quality; it can be used in a 'progressive' manner to save on computational time and increase usability. Further, it can be used to take advantage of multiple popular edge detection algorithms. There is still a continuing research effort to develop new and effective edge detection algorithms. Even though extraction of the edges is a key step in image processing and, there is no single, reliable and efficient metric to evaluate the quality of an edge detector. We introduce an original method that is based on median-interpolation of the edge map for image reconstruction. This image estimation technique is useful for evaluation of the edge map and hence the edge detector. An improvised quantitative metric for the assessment of the reconstructed image is also presented. We also introduce techniques to operate the feedback control in the edge detection system. This results in several advantages such as automation of parameterization and comparison of edge detectors. The operation of the measure is established on varied images using common edge detection algorithms as well as the one based on Boolean derivatives. The uses of the measure for an assortment of purposes are demonstrated and these are backed by visual assessment as well as some distance-based error functions applied on synthetic images. The comprehensive analysis of our algorithm includes testing it on images of various objects from different sources and images used for diverse applications. Our test image database contains images used for medical-diagnostic, security and consumer purposes besides other categories.