Made in the humanities: Dual integral invariants for efficient edge detection

Abstract

Abstract Motivated by the demand for robust character extraction from ancient documents with Script in 3D like cuneiform tablets, we are developing curvature based filter algorithms using integral invariants. While previous work was focused on analyzing 3D-models i. e. irregular triangular meshs in ℝ3, we introduce a fast, efficient adaption for edge detection in raster images. It is an alternative to the Canny edge detector algorithm and other complex algorithms using first and second order derivative filters. Our approach consists of two steps using (i) zero-crossings of volume integral invariants and (ii) surface integral invariants to discard false positives introduced by noise. The runtime of these Dual Integral Invariants (DII) is comparable with Difference of Gaussian filtering and it is independent of the number and length of edges. An additional benefit is the constant execution time as line tracing is not necessary. As the proposed algorithm has no smoothing included it preserves smaller features than recent variants of the Canny edge detector. We use artificial data sets with and without a known amount of noise to validate the accuracy of our method in comparison with operators supplied by the OpenCV library. The equidistant spacing of raster images allows fast estimation of the integral invariants based on filter masks like Roberts, Scharr and Kirsch. We show the results on well-known standard test images and synthetic data.