A Contour Tracing Algorithm that Avoids Duplicate Tracing Common Boundaries between Regions

The authors of this paper have developed a series of techniques on automatic function approximation of raster images, including references published in this journal. In our techniques, contours are traced and their shapes are approximated by a combination of functions including straight line, arc, and quadratic curve. Because our previous works targeted mainly bi-level or two-labeled images, conventional contour tracing algorithms were sufficient. However, when these earlier algorithms were applied to images of multiple labels, the problem of duplicate tracing common boundaries between regions occurred, adversely affecting the result of function approximation. In this paper, we focus on contour tracing and propose an algorithm that can correctly trace all boundaries including those common to neighboring regions without duplication. Our originality lies in the tracing steps that follow after boundary points where three or more labels meet are detected. Every boundary that branches from such points is recorded and traced in succession while avoiding duplicate tracing. As a result, common boundaries can be shared, which is not possible with conventional algorithms.