Convexity is an important geometric property of many natural and man-made structures. Prior research has shown that it is imperative to many perceptual-organization and imageunderstanding tasks. This paper presents a new grouping method for detecting convex structures from noisy images in a globally optimal fashion. Particularly, this method combines both region and boundary information: the detected structural boundary is closed and well aligned with detected edges while the enclosed region has good intensity homogeneity. We introduce a ratio-form cost function for measuring the structural desirability, which avoids a possible bias to detect small structures. A new fragment-pruning algorithm is developed to achieve the structural convexity. The proposed method can also be extended to detect open boundaries, which correspond to the structures that are partially cropped by the image perimeter, and incorporate a humancomputer interaction for detecting a convex boundary around a specifi...
Joachim S. Stahl, Song Wang