Automatic Fitting of Digitised Contours at Multiple Scales through Curvature Scale Space

Abstract

The Curvature Scale Space (CSS) technique has been used in conjunction with Hermite curves for automatic fitting of digitised contours at multiple scales. CSS is a powerful contour shape descriptor which is expected to be in the MPEG-7 standard. A parametric representation of the input contour is convolved with Gaussian functions in order to obtain multi-scale descriptions of the contour. Curvature can be computed directly at each point of the smoothed contours. As a result, a set of curvature zero-crossing points can be recovered from each smoothed contour. Hermite curves were used since each Hermite curve is defined by two endpoints and the tangent vectors at those points. No points external to the input contour are required for Hermite curves. Hermite endpoints are defined as consecutive curvature zero-crossing points extracted at multiple scales using the CSS method. Hermite tangent vectors can also be determined using the CSS technique. The only data stored are the endpoints and the tangent vectors needed by the Hermite curves in order to arrive at an approximate reconstruction of the original contour. Approximation Error and Compression Ratio are computed at each scale. The graph of compression ratio as a function of approximation error is smoothed to remove noise and small fluctuations. The bending point of that function is then defined as the largest maximum of its second derivative. The bending point can be considered as the boundary between the mostly vertical and the mostly horizontal segments of the graph. It can be used for automatic selection of an optimal scale.