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

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

A normalized mirrored correlation measure for data symmetry detection

Symmetry detection algorithms are enjoying a renovated interest in the scientific community, fueled by recent advancements in computer vision and computer graphics applications. This paper is inspired by recent efforts in building a symmetric object detection system in natural images. In particular, it is first shown how correlation can be a core operator that allows finding local reflection symmetry points in 1-D sequences that are optimal in an energetic sense. Then, the importance of 2-D correlation in natural images to correctly align the symmetric object axis is demonstrated. Using the correlation as described is crucial in boosting the performance of the system, as proven by the results on a standard dataset

Global Bilateral Symmetry Detection Using Multiscale Mirror Histograms

In recent years, there has been renewed interest in bilateral symmetry detection in images. It consists in detecting the main bilateral symmetry axis inside artificial or natural images. State-of-the-art methods combine feature point detection, pairwise comparison and voting in Hough-like space. In spite of their good performance, they fail to give reliable results over challenging real-world and artistic images. In this paper, we propose a novel symmetry detection method using multi-scale edge features combined with local orientation histograms. An experimental evaluation is conducted on public datasets plus a new aesthetic-oriented dataset. The results show that our approach outperforms all other concurrent methods

Multiple Reflection Symmetry Detection via Linear-Directional Kernel Density Estimation

Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing kernel over different voting maps in the polar coordinate system to detect symmetry peaks, which split the regions of symmetry axis candidates in inefficient way. We propose a reliable voting representation based on weighted linear-directional kernel density estimation, to detect multiple symmetries over challenging real-world and synthetic images. Experimental evaluation on two public datasets demonstrates the superior performance of the proposed algorithm to detect global symmetry axes respect to the major image shapes

Objective quality prediction of image retargeting algorithms

Quality assessment of image retargeting results is useful when comparing different methods. However, performing the necessary user studies is a long, cumbersome process. In this paper, we propose a simple yet efficient objective quality assessment method based on five key factors: i) preservation of salient regions; ii) analysis of the influence of artifacts; iii) preservation of the global structure of the image; iv) compliance with well-established aesthetics rules; and v) preservation of symmetry. Experiments on the RetargetMe benchmark, as well as a comprehensive additional user study, demonstrate that our proposed objective quality assessment method outperforms other existing metrics, while correlating better with human judgements. This makes our metric a good predictor of subjective preference

Gestalt Algebra - A Proposal for the Formalization of Gestalt Perception and Rendering

Gestalt Algebra gives a formal structure suitable for describing complex patterns in the image plain. This can be useful for recognizing hidden structure in images. The work at hand refers to the laws of perceptual psychology. A manifold called the Gestalt Domain is defined. Next to the position in 2D it also contains an orientation and a scale component. Algebraic operations on it are given for mirror symmetry as well as organization into rows. Additionally the Gestalt Domain contains an assessment component, and all the meaning of the operations implementing the Gestalt-laws is realized in the functions giving this component. The operation for mirror symmetry is binary, combining two parts into one aggregate as usual in standard algebra. The operation for organization into rows, however, combines n parts into an aggregate, where n may well be more than two. This is algebra in its more general sense. For recognition, primitives are extracted from digital raster images by Lowe’s Scale Invariant Feature Transform (SIFT). Lowe’s key-point descriptors can also be utilized. Experiments are reported with a set of images put forth for the Computer Vision and Pattern Recognition Workshops (CVPR) 2013 symmetry contest

Mathematical mirroring for identification of local symmetry centers in microscopic images local symmetry detection in FIJI

Symmetry is omnipresent in nature and we encounter symmetry routinely in our everyday life. It is also common on the microscopic level, where symmetry is often key to the proper function of core biological processes. The human brain is exquisitely well suited to recognize such symmetrical features with ease. In contrast, computational recognition of such patterns in images is still surprisingly challenging. In this paper we describe a mathematical approach to identifying smaller local symmetrical structures within larger images. Our algorithm attributes a local symmetry score to each image pixel, which subsequently allows the identification of the symmetrical centers of an object. Though there are already many methods available to detect symmetry in images, to the best of our knowledge, our algorithm is the first that is easily applicable in ImageJ/FIJI. We have created an interactive plugin in FIJI that allows the detection and thresholding of local symmetry values. The plugin combines the different reflection symmetry axis of a square to get a good coverage of reflection symmetry in all directions. To demonstrate the plugins potential, we analyzed images of bacterial chemoreceptor arrays and intracellular vesicle trafficking events, which are two prominent examples of biological systems with symmetrical patterns.Microbial Biotechnolog