ON SYMMETRY: A FRAMEWORK FOR AUTOMATED SYMMETRY DETECTION

Symmetry has weaved itself into almost all fabrics of science, as well as in arts, and has left an indelible imprint on our everyday lives. And, in the same manner, it has pervaded a wide range of areas of computer science, especially computer vision area, and a copious amount of literature has been produced to seek an algorithmic way to identify symmetry in digital data. Notwithstanding decades of endeavor and attempt to have an efficient system that can locate and recover symmetry embedded in real-world images, it is still challenging to fully automate such tasks while maintaining a high level of efficiency. The subject of this thesis is symmetry of imaged objects. Symmetry is one of the non-accidental features of shapes and has long been (maybe mistakenly) speculated as a pre-attentive feature, which improves recognition of quickly presented objects and reconstruction of shapes from incomplete set of measurements. While symmetry is known to provide rich and useful geometric cues to computer vision, it has been barely used as a principal feature for applications because figuring out how to represent and recognize symmetries embedded in objects is a singularly difficult task, both for computer vision and for perceptual psychology. The three main problems addressed in the dissertation are: (i) finding approximate symmetry by identifying the most prominent axis of symmetry out of an entire region, (ii) locating bilaterally symmetrical areas from a scene, and (iii) automating the process of symmetry recovery by solving the problems mentioned above. Perfect symmetries are rare in the extreme in natural images and symmetry perception in humans allows for qualification so that symmetry can be graduated based on the degree of structural deformation or replacement error. There have been many approaches to detect approximate symmetry by searching an optimal solution in a form of an exhaustive exploration of the parameter space or surmising the center of mass. The algorithm set out in this thesis circumvents the computationally intensive operations by using geometric constraints of symmetric images, and assumes no prerequisite knowledge of the barycenter. The results from an extensive set of evaluation experiments on metrics for symmetry distance and a comparison of the performance between the method presented in this thesis and the state of the art approach are demonstrated as well. Many biological vision systems employ a special computational strategy to locate regions of interest based on local image cues while viewing a compound visual scene. The method taken in this thesis is a bottom-up approach that causes the observer favors stimuli based on their saliency, and creates a feature map contingent on symmetry. With the help of summed area tables, the time complexity of the proposed algorithm is linear in the size of the image. The distinguished regions are then delivered to the algorithm described above to uncover approximate symmetry

Estimating Symmetry/Asymmetry in the Human Torso: A Novel Computational Method

Asymmetry in human body has largely been based on bilateral traits and/or subjective estimates, with potential usage in fields such as medicine, rehabilitation and apparel product design. In case of apparel, asymmetry in human body has been measured primarily by estimating differential linear measurement of bilateral traits. However, the characteristics of asymmetry can be better understood and be useful for clinicians and designers if it is quantified by considering the whole 3D surface. To address the prevailing issues in measuring asymmetry objectively, this research attempts to develop a novel method to quantify asymmetry that is robust, effective and non-invasive in operation. The method discussed here uses 3D scans of human torso to estimate asymmetry as a numerical index. Furthermore, using skeletal landmarks, twist and tilt measurements of the torsos are computed numerically. Together, these three measures can characterize the asymmetric/symmetric nature of a human torso. The approach taken in this research uses cross sections of torso to estimate local plane of symmetry that equi-divides a given cross section on the basis of its area, and connecting those planes to form a global surface that divides the torso volumetrically. The computational approach in estimating the area of cross section is based on the Green's theorem. The developed method was validated by both testing it on a known geometric model and by comparing the estimated index with subjective ratings by experts. This method has potential applications in various fields requiring characterizing asymmetry i.e., in case of scoliosis patients as diagnostic tool or an evaluation metric for rehabilitation efficiency, for body builders, and fashion models as an evaluation tool.Design, Housing and Merchandisin

A study of Symmetric and Repetitive Structures in Image-Based Modeling

Ph.DDOCTOR OF PHILOSOPH

Augmented Reality and Artificial Intelligence in Image-Guided and Robot-Assisted Interventions

In minimally invasive orthopedic procedures, the surgeon places wires, screws, and surgical implants through the muscles and bony structures under image guidance. These interventions require alignment of the pre- and intra-operative patient data, the intra-operative scanner, surgical instruments, and the patient. Suboptimal interaction with patient data and challenges in mastering 3D anatomy based on ill-posed 2D interventional images are essential concerns in image-guided therapies. State of the art approaches often support the surgeon by using external navigation systems or ill-conditioned image-based registration methods that both have certain drawbacks. Augmented reality (AR) has been introduced in the operating rooms in the last decade; however, in image-guided interventions, it has often only been considered as a visualization device improving traditional workflows. Consequently, the technology is gaining minimum maturity that it requires to redefine new procedures, user interfaces, and interactions. This dissertation investigates the applications of AR, artificial intelligence, and robotics in interventional medicine. Our solutions were applied in a broad spectrum of problems for various tasks, namely improving imaging and acquisition, image computing and analytics for registration and image understanding, and enhancing the interventional visualization. The benefits of these approaches were also discovered in robot-assisted interventions. We revealed how exemplary workflows are redefined via AR by taking full advantage of head-mounted displays when entirely co-registered with the imaging systems and the environment at all times. The proposed AR landscape is enabled by co-localizing the users and the imaging devices via the operating room environment and exploiting all involved frustums to move spatial information between different bodies. The system's awareness of the geometric and physical characteristics of X-ray imaging allows the exploration of different human-machine interfaces. We also leveraged the principles governing image formation and combined it with deep learning and RGBD sensing to fuse images and reconstruct interventional data. We hope that our holistic approaches towards improving the interface of surgery and enhancing the usability of interventional imaging, not only augments the surgeon's capabilities but also augments the surgical team's experience in carrying out an effective intervention with reduced complications

Detecting bilateral symmetry in perspective

A method is presented for efficiently detecting bilateral symmetry on planar surfaces under perspective projection. The method is able to detect local or global symmetries, locate symmetric surfaces in complex backgrounds, and detect multiple incidences of symmetry. Symmetry is simultaneously evaluated across all locations, scales, orientations and under perspective skew. Feature descriptors robust to local affine distortion are used to match pairs of symmetric features. Feature quadruplets are then formed from these symmetric feature pairs. Each quadruplet hypothesises a locally planar 3D symmetry that can be extracted under perspective distortion. The method is posed independently of a specific feature detector or descriptor. Results are presented demonstrating the efficacy of the method for detecting bilateral symmetry under perspective distortion. Our unoptimised Matlab implementation, running on a standard PC, requires of the order of 20 seconds to process images with 1,000 feature points