Recognition of human body posture from a cloud of 3D data points using wavelet transform coefficients

Addresses the problem of recognizing a human body posture from a cloud of 3D points acquired by a human body scanner. Motivated by finding a representation that embodies a high discriminatory power between posture classes, a new type of feature is suggested, namely the wavelet transform coefficients (WTC) of the 3D data-point distribution projected on to the space of spherical harmonics. A feature selection technique is developed to find those features with high discriminatory power. Integrated within a Bayesian classification framework and compared with other standard features, the WTC showed great capability in discriminating between close postures. The qualities of the WTC features were also reflected in the experimental results carried out with artificially generated postures, where the WTC obtained the best classification rat

Advances in Manipulation and Recognition of Digital Ink

Handwriting is one of the most natural ways for a human to record knowledge. Recently, this type of human-computer interaction has received increasing attention due to the rapid evolution of touch-based hardware and software. While hardware support for digital ink reached its maturity, algorithms for recognition of handwriting in certain domains, including mathematics, are lacking robustness. Simultaneously, users may possess several pen-based devices and sharing of training data in adaptive recognition setting can be challenging. In addition, resolution of pen-based devices keeps improving making the ink cumbersome to process and store. This thesis develops several advances for efficient processing, storage and recognition of handwriting, which are applicable to the classification methods based on functional approximation. In particular, we propose improvements to classification of isolated characters and groups of rotated characters, as well as symbols of substantially different size. We then develop an algorithm for adaptive classification of handwritten mathematical characters of a user. The adaptive algorithm can be especially useful in the cloud-based recognition framework, which is described further in the thesis. We investigate whether the training data available in the cloud can be useful to a new writer during the training phase by extracting styles of individuals with similar handwriting and recommending styles to the writer. We also perform factorial analysis of the algorithm for recognition of n-grams of rotated characters. Finally, we show a fast method for compression of linear pieces of handwritten strokes and compare it with an enhanced version of the algorithm based on functional approximation of strokes. Experimental results demonstrate validity of the theoretical contributions, which form a solid foundation for the next generation handwriting recognition systems

Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution

Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [Ellis, Haven, Turkington, Nonlin., 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D, 237, 1998 (2008)]. They can provide a small-scale parametrization of 2D turbulence or serve as numerical algorithms to compute maximum entropy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows.Comment: 21 pages, 9 figure

The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations

This survey article begins with a discussion of the original form of the Strominger-Yau-Zaslow conjecture, surveys the state of knowledge concering this conjecture, and explains how thinking about this conjecture naturally leads to the program initiated by the author and Bernd Siebert to study mirror symmetry via degenerations of Calabi-Yau manifolds and log structures.Comment: 44 pages, to appear in the Proceedings of the 2005 AMS Symposium on Algebraic Geometry, Seattl

The Role of Transient Vibration of the Skull on Concussion

Concussion is a traumatic brain injury usually caused by a direct or indirect blow to the head that affects brain function. The maximum mechanical impedance of the brain tissue occurs at 450±50 Hz and may be affected by the skull resonant frequencies. After an impact to the head, vibration resonance of the skull damages the underlying cortex. The skull deforms and vibrates, like a bell for 3 to 5 milliseconds, bruising the cortex. Furthermore, the deceleration forces the frontal and temporal cortex against the skull, eliminating a layer of cerebrospinal fluid. When the skull vibrates, the force spreads directly to the cortex, with no layer of cerebrospinal fluid to reflect the wave or cushion its force. To date, there is few researches investigating the effect of transient vibration of the skull. Therefore, the overall goal of the proposed research is to gain better understanding of the role of transient vibration of the skull on concussion. This goal will be achieved by addressing three research objectives. First, a MRI skull and brain segmentation automatic technique is developed. Due to bones’ weak magnetic resonance signal, MRI scans struggle with differentiating bone tissue from other structures. One of the most important components for a successful segmentation is high-quality ground truth labels. Therefore, we introduce a deep learning framework for skull segmentation purpose where the ground truth labels are created from CT imaging using the standard tessellation language (STL). Furthermore, the brain region will be important for a future work, thus, we explore a new initialization concept of the convolutional neural network (CNN) by orthogonal moments to improve brain segmentation in MRI. Second, the creation of a novel 2D and 3D Automatic Method to Align the Facial Skeleton is introduced. An important aspect for further impact analysis is the ability to precisely simulate the same point of impact on multiple bone models. To perform this task, the skull must be precisely aligned in all anatomical planes. Therefore, we introduce a 2D/3D technique to align the facial skeleton that was initially developed for automatically calculating the craniofacial symmetry midline. In the 2D version, the entire concept of using cephalometric landmarks and manual image grid alignment to construct the training dataset was introduced. Then, this concept was extended to a 3D version where coronal and transverse planes are aligned using CNN approach. As the alignment in the sagittal plane is still undefined, a new alignment based on these techniques will be created to align the sagittal plane using Frankfort plane as a framework. Finally, the resonant frequencies of multiple skulls are assessed to determine how the skull resonant frequency vibrations propagate into the brain tissue. After applying material properties and mesh to the skull, modal analysis is performed to assess the skull natural frequencies. Finally, theories will be raised regarding the relation between the skull geometry, such as shape and thickness, and vibration with brain tissue injury, which may result in concussive injury