Direct computation of differential invariants of image contours from shading

We present a framework combining differential geometry and scale-space to show that local geometric invariants of image contours such as tangent, curvature and derivative of curvature can be computed directly and stably from the raw image itself. To solve the problem of noise amplification by differential operations, scale-parameterized local kernels are used to replace differential operations by integral operations, which can be carried out accurately when we adopt a continuous image model. We also show that tangent estimation along contours can be made quite accurately using only eight tangent estimators (a π/4 quantization) when contour location is known, and high precision and efficiency in computation can be achieved for each of the invariants regardless of the differential order involved