Shape plays an important role in Computer Vision, with applications in problems such as matching, object recognition, and classification. However, to the best of our knowledge the question as to whether there is a set of elementary planar shapes that appear commonly in the world around us has never been asked within the literature.
If such a set exists, then the elementary shapes could play a similar role in shape analysis as the primary colours do in colour analysis. It is well known that a range of colours can be made by combing by a set of primary colours, which are red, green and blue. And feature descriptors based on colour are very popular in image processing and computer vision problems. Similarly, a complex shape or region also can be fitted by combination of simple shapes, such as a Tangram.
We describe an experiment designed to test the following hypothesis: a significant fraction of regions in image segmentations can be classified as one of a few primitive shapes. Not wishing to force regions into classes, we developed a fully unsupervised, non-parametric classifier designed to find clusters of a size greater than would be expected if the shape of regions were randomly generated. We used two different 'shape spaces' (i.e. shape descriptors), three different segmentation methods, and three image databases. The result was that primitive shapes (up to an affine transform) such as 'triangle', 'square', and 'circle' account for between 50% and 80% of regions.
Fig. Matrices of final results. In each matrix element the shapes are ordered by descending
frequency from top-left to bottom-right. (a) Each entry shows the shape icons yielded by
different databases, different segmentation methods. (b) Shape icons for different segmentation methods yielded by combining all three databases, different segmentation methods. (c): Final grouping result by combing all databases and segmentations. The number of each prime shape is plotted in each corresponding icon. The total number of segmented regions, classified or not, is 56992