Fluctuating asymmetry consists of random deviations from perfect symmetry in populations of organisms. It is a measure of developmental noise, which reflects a population’s average state of adaptation and coadaptation. Moreover, it increases under both environmental and genetic stress, though responses are often inconsistent. Researchers base studies of fluctuating asymmetry upon deviations from bilateral, radial, rotational, dihedral, translational, helical, and fractal symmetries. Here, we review old and new methods of measuring fluctuating asymmetry, including measures of dispersion, landmark methods for shape asymmetry, and continuous symmetry measures. We also review the theory, developmental origins, and applications of fluctuating asymmetry, and attempt to explain conflicting results. In the process, we present examples from the literature, and from our own research at “Evolution Canyon” and elsewhere.

In the arts and sciences, as well as in our daily lives, symmetry has made a profound and lasting impact. Likewise, a computational treatment of symmetry and group theory (the ultimate mathematical formalization of symmetry) has the potential to play an important role in computational sciences. Though the term computational symmetry was formally defined a decade ago by the first author, referring to algorithmic treatment of symmetries, seeking symmetry from digital data has been attempted for over four decades. Computational symmetry on real world data turns out to be challenging enough that, after decades of effort, a fully automated symmetry–savvy system remains elusive for real world applications. The recent resurging interests in computational symmetry for computer vision and computer graphics applications have shown promising results. Recognizing the fundamental relevance and potential power that computational symmetry affords, we offer this survey to the computer vision and computer graphics communities. This survey provides a succinct summary of the relevant mathematical theory, a historic perspective of some important symmetry-related ideas, a partial yet timely report on the state of the arts symmetry detection algorithms along with its first quantitative benchmark, a diverse set of real world applications, suggestions for future directions and a comprehensive reference list.

Automating fall risk assessment, in an efficient, non-invasive manner, specifically in the elderly population, serves as an efficient means for implementing wide screening of individuals for fall risk and determining their need for participation in fall prevention programs. We present an automated and efficient system for fall risk assessment based on a multi-depth camera human motion tracking system, which captures patients performing the well-known and validated Berg Balance Scale (BBS). Trained machine learning classifiers predict the patient’s 14 scores of the BBS by extracting spatio-temporal features from the captured human motion records. Additionally, we used machine learning tools to develop fall risk predictors that enable reducing the number of BBS tasks required to assess fall risk, from 14 to 4–6 tasks, without compromising the quality and accuracy of the BBS assessment. The reduced battery, termed Efficient-BBS (E-BBS), can be performed by physiotherapists in a traditional setting or deployed using our automated system, allowing an efficient and effective BBS evaluation. We report on a pilot study, run in a major hospital, including accuracy and statistical evaluations. We show the accuracy and confidence levels of the E-BBS, as well as the average number of BBS tasks required to reach the accuracy thresholds. The trained E-BBS system was shown to reduce the number of tasks in the BBS test by approximately 50% while maintaining 97% accuracy. The presented approach enables a wide screening of individuals for fall risk in a manner that does not require significant time or resources from the medical community. Furthermore, the technology and machine learning algorithms can be implemented on other batteries of medical tests and evaluations.

Although camera and sensor noise are often disregarded, assumed negligible or dealt with in the context of denoising, in this paper we show that significant information can actually be deduced from camera noise about the captured scene and the objects within it. Specifically, we deal with depth cameras and their noise patterns. We show that from sensor noise alone, the object’s depth and location in the scene can be deduced. Sensor noise can indicate the source camera type, and within a camera type the specific device used to acquire the images. Furthermore, we show that noise distribution on surfaces provides information about the light direction within the scene as well as allows to distinguish between real and masked faces. Finally, we show that the size of depth shadows (missing depth data) is a function of the object’s distance from the background, its distance from the camera and the object’s size. Hence, can be used to authenticate objects location in the scene. This paper provides tools and insights into what can be learned from depth camera sensor noise.