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The importance of measuring the complexity of shapes can be seen by the wide range of its application such as computer vision, robotics, cognitive studies, eye tracking, and psychology. However, it is very challenging to define an accurate and precise metric to measure the complexity of the shapes. In this paper, we explore different notions of shape complexity, drawing from established work in mathematics, computer science, and computer vision. We integrate results from user studies with quantitative analyses to identify three measures that capture important axes of shape complexity, out of a list of almost 300 measures previously considered in the literature. We then explore the connection between specific measures and the types of complexity that each one can elucidate. Finally, we contribute a dataset of both abstract and meaningful shapes with designated complexity levels both to support our findings and to share with other researchers. [ABSTRACT FROM AUTHOR]

Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting since, by carefully exploiting problem structure, they often provide nontrivial guarantees concerning solution quality. In this paper, we review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo, the mid-level problem of interactive object segmentation, and the high-level problem of model-based recognition. [ABSTRACT FROM PUBLISHER]