Unified detection of skewed rotation, reflection and translation symmetries from affine invariant contour features

• A unified framework is proposed for detecting different symmetries on real-world images.
• Affine invariant contour matching is used to find correspondence under skewed imaging.
• A sign change criterion is proposed to classify matching pairs for different symmetries.
• Novel schemes such as that based on short line segments are proposed for symmetry voting.
• Different symmetries are detected simultaneously or separately with desired performance.

Symmetry detection is significant for object detection and recognition since symmetries are salient cues for distinguishing geometrical structures from cluttered backgrounds. This paper proposes a unified framework to detect rotation, reflection and translation symmetries simultaneously on unsegmented real-world images. The detection is performed based on affine invariant contour features, and is applicable under skewed imaging with distortions. Contours on a natural image are first matched to each other to find affine invariant matching pairs, which are then classified into three groups using a sign change criterion corresponding to the three types of symmetries. The three groups are used to vote for the corresponding symmetries: the voting for rotation utilizes a scheme of short line segments; the voting for reflection is based on a parameterization of axis equation, and the voting for translation uses a cascade-like approach. Experimental results of real-world images are provided with quantitative evaluations, validating that the proposed framework achieves desired performance.