Extracting Meaningful Curves from Images

The set of level lines of an image (isophotes) or topographic map is a complete and contrast invariant representation of an image. Level lines are ordered by inclusion in a tree structure. These two structure properties make level lines excellent candidates to shape representatives. However, some complexity issues have to be handled: The number of level lines in eight-bits encoded images of size 512×512 is typically 10⁵. Most of them are very small lines due to noise or micro-texture. So the stable level lines must be selected, namely the ones that are likely to correspond to image contours. The starting point is the MSER method, a variant of the Monasse and Guichard Fast Level Set Transform. The MSER selects a set of level lines which are local extrema of contrast. This method will be put in the Helmholtz framework, following the a contrario boundary detection algorithm by Desolneux, Moisan and Morel [51], [54] and two powerful recent variants. The experiments in this chapter will show that selecting the most meaningful level lines reduces their number by a factor 100 without significant shape contents loss.

A method which selects one out of hundred level lines in the image without significant information loss is necessarily sophisticated. Sect. 2.1 briefly reviews the level line tree of a digital image. Sect. 2.2 describes a first way to extract well contrasted level lines, the MSER method. Sect. 2.3 makes an account of the Desolneux et al. maximal meaningful boundaries and Sect. 2.4 gives a mathematical justification which was actually missing in the original theory. Sect. 2.5 is devoted to a multiscale extension which avoids missing boundaries because of high noise level and Sect. 2.6 deals with the so called “blue sky” effect which can lead to over-detections in textured parts of the image.