Robust Curvature Estimation by Finding Optimal Circular Segments in Orientation Space

We have developed a new, robust, curvature estimator. It is based on ”fitting” circular segments to a curve using a generalised Radon transform. The key step in the approach is that the fitting operation is not done in the original image, but in a transformed version, called Orientation Space. The original curve is transformed into another curve in Orientation Space. Apart from the original spatial dimensions, Orientation Space has one extra dimension: orientation. A given point on the curve in Orientation Space contains information both about the original position of the point, but also about the orientation of that point. This explicit representation of orientation allows us to incorporate it as a contraint in the fitting stage, where curves corresponding to circular segments in the original image are fitted to the data. The estimated curvature is the reciprocal of the radius of the best fitting segment. The method performs well on noisy (synthetic) data and should work correctly on intersecting curves as well. The performance of the estimator has not yet been compared to existing approaches in the litature. The method is a demonstration of a novel, general, approach to incorporating constraints in the Radon Transform.