A Min-Cover Approach for Finding Salient Curves

We consider the problem of deriving a global interpretation of an image in terms of a small set of smooth curves. The problem is posed using a statistical model for images with multiple curves. Besides having important applications to edge detection and grouping the curve finding task is a special case of a more general problem, where we want to explain the whole image in terms of a small set of objects. We describe a novel approach for estimating the content of scenes with multiple objects using a min-cover framework that is simple and powerful. The min-cover problem is NP-hard but there is a good approximation algorithm that sequentially selects objects minimizing a "cost per pixel" measure. In the case of curve detection we use a type of best-first search to quickly find good curves for the covering algorithm. The method integrates image data over long curves without relying on binary feature detection. We have applied the curve detection method for finding object boundaries in natural scenes and measured its performance using the Berkeley segmentation dataset.