On reflection symmetry in natural images

Many new symmetry detection algorithms have been recently developed, thanks to an interest revival on computational symmetry for computer graphics and computer vision applications. Notably, in 2013 the IEEE CVPR Conference organized a dedicated workshop and an accompanying symmetry detection competition. In this paper we propose an approach for symmetric object detection that is based both on the computation of a symmetry measure for each pixel and on saliency. The symmetry value is obtained as the energy balance of the even-odd decomposition of a patch w.r.t. each possible axis. The candidate symmetry axes are then identified through the localization of peaks along the direction perpendicular to each considered axis orientation. These found candidate axes are finally evaluated through a confidence measure that also allow removing redundant detected symmetries. The obtained results within the framework adopted in the aforementioned competition show significant performance improvement

Image symmetries: The right balance between evenness and perception

A recent and fascinating interest in computational symmetry for computer vision and computer graphics applications has led to a remarkable realization of new symmetry detection algorithms. Such a concern is culminated in a symmetry detection competition as a workshop affiliated with the 2011 and 2013 CVPR Conferences. In this paper, we propose a method based on the computation of the symmetry level associated to each pixel. Such a value is determined through the energy balance of the even/odd decomposition of a patch with respect to a central axis (which is equivalent to estimate the middle point of a row-wise convolution). Peaks localization along the perpendicular direction of each angle allows to identify possible symmetry axes. The evaluation of a feature based on gradient information allows to establish a classification confidence for each detected axis. By adopting the aforementioned rigorous validation framework, the proposed method indicates significant performance increase

Symmetry Detection of Rational Space Curves from their Curvature and Torsion

We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly faster, simpler, and more general than an earlier method addressing a similar problem. To support this claim, we present an analysis of the arithmetic complexity of the algorithm and timings from an implementation in Sage.Comment: 25 page

SAVOIAS: A Diverse, Multi-Category Visual Complexity Dataset

Visual complexity identifies the level of intricacy and details in an image or the level of difficulty to describe the image. It is an important concept in a variety of areas such as cognitive psychology, computer vision and visualization, and advertisement. Yet, efforts to create large, downloadable image datasets with diverse content and unbiased groundtruthing are lacking. In this work, we introduce Savoias, a visual complexity dataset that compromises of more than 1,400 images from seven image categories relevant to the above research areas, namely Scenes, Advertisements, Visualization and infographics, Objects, Interior design, Art, and Suprematism. The images in each category portray diverse characteristics including various low-level and high-level features, objects, backgrounds, textures and patterns, text, and graphics. The ground truth for Savoias is obtained by crowdsourcing more than 37,000 pairwise comparisons of images using the forced-choice methodology and with more than 1,600 contributors. The resulting relative scores are then converted to absolute visual complexity scores using the Bradley-Terry method and matrix completion. When applying five state-of-the-art algorithms to analyze the visual complexity of the images in the Savoias dataset, we found that the scores obtained from these baseline tools only correlate well with crowdsourced labels for abstract patterns in the Suprematism category (Pearson correlation r=0.84). For the other categories, in particular, the objects and advertisement categories, low correlation coefficients were revealed (r=0.3 and 0.56, respectively). These findings suggest that (1) state-of-the-art approaches are mostly insufficient and (2) Savoias enables category-specific method development, which is likely to improve the impact of visual complexity analysis on specific application areas, including computer vision.Comment: 10 pages, 4 figures, 4 table