Line drawings are easy to recognize, although the only information tc, the visual system is the contour itself. Starting from information theory and a theory of decomposition in parts, we investigated whether certain regions of such a contour are perceptually more relevant than others, using a deletion detection paradigm. In this paradigm, high detectability means poor contour integration, and vice verse. Regions of interest were curvature singularities, namely positive maxima (M+), negative minima (m-) and inflection points (I), of smooth, closed contours. In Experiment 1, we performed a first exploration of the detectability of deletions around these three types of curvature singularities. M+ deletions were easier to detect than the deletions around the other two singularities, a result that is explained using a post hoc combination of both mentioned theoretical frameworks. In Experiment 2, we replicated these findings using figure-background reversal, so that the same physical deletions could either be M+ or m-. Again, the M+ deletions were easier to detect than m- deletions. Although both types of singularities involve regions of high curvature changes, they differ in that m- deletions create gaps that concur with spontaneous segmentation.