Using multiscale top points in image matching

We discuss the feasibility of using singular points in a scale space representation (referred to as top points) for image matching purposes. These points are easily extracted from the scale space of an image and they form a compact description of the image. The image matching problem thus becomes a point cloud matching problem. This is related to the transportation problem known from linear optimization and we solve it by using an earth mover´s distance algorithm. To match points in scale space, a distance measure is needed, as Euclidean distance no longer applies. We suggest a metric that can be used in scale space and show that it indeed performs better than a Euclidean distance measure. To distinguish between stable and unstable top points, we derive a stability norm based on the total variation norm which only depends on the second order derivatives at the top point. To improve matching results further, we show that other features at the top points can also increase the accuracy of matching.