Analysis of symmetric patterns in images

Abstract

The computational detection of symmetry is of large importance not only to model human vision, but to leverage the structural information it carries. Due to the complexity of the problem, researchers tackle automated symmetry detection as a search rather than a model-based approach in most of the cases.

The detection of symmetry has found several applications including segmentation, gait analysis, interest-point detection, saliency models and human pose tracking amongst others. Despite the variety of approaches, the detection of symmetry is still an open area of research. In this thesis, symmetry perception and detection algorithms are directly related to Marr’s stages of vision.

Feature-based symmetry detection methods tend to over-perform other approaches, nevertheless, they are computationally demanding. These are reliant on the presence of matched pairs of features, therefore they benefit from the abundance of such points; this implies that a trade-off between performance and computation time must be found. Here, the detection of large sets of features and the computation time for feature based symmetry detection algorithms are addressed.

A new procedure for feature based symmetry detection is introduced. We make use of the efficient binary descriptors, allowing for a drastic reduction on the computation times. Moreover, we use a density-based approach to detect axes of symmetry in the parameter space; this augments resolution and provides more flexibility for the detection.

Two new feature detection methods are presented. The Locally Contrasting Keypoints (LOCKY) is a novel blob-detector aimed at reducing computation times. The detection is achieved with an innovative non-deterministic low-level operator called the Brightness Clustering Transform (BCT). The BCT can be thought as a coarse-to-fine search through scale spaces for the true derivative of the image; it also mimics trans-saccadic perception of human vision. LOCKY shows good robustness to image transformations included in the Oxford affine-covariant regions dataset, and is amongst the fastest affine-covariant feature detectors.

Unsupervised representation learning enables computers to learn visual cues from unlabelled data, obviating the need for hand-crafted feature models. The second feature detector is a novel technique to find rotation-invariant structures using an unsupervised representation learning strategy. This is accomplished by mapping image-patches into a rotation-invariant space built with the Bessel-Fourier moments. We analyse this space in terms of the symmetry of features and categorise them into three groups, non-symmetric, symmetric and composite-symmetric. Feature-maps are created by comparing patches in an image against the feature models, non-maxima suppression is performed afterwards. The detected features show very competitive results on repeatability tests compared with state of the art detectors. Moreover our approach can recognise multiple structures therefore, the user can substantially increase the amount of detected features in a controlled manner.

Using the methods presented in this thesis, symmetry detection computation times are drastically reduced by approximately ten-fold compared to other state of the art approaches. The use unsupervised learning for the rotation-invariant detection of structures,
also yields an improvement on the symmetry detection performance measured against the state of the art.

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Identifiers

ORCID for Mark Nixon: orcid.org/0000-0002-9174-5934

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