Model Based Probabilistic Piecewise Curve Approximation

Publication in the conference proceedings of EUSIPCO, Bucharest, Romania, 201

The statistical properties and coding of handwriting and hand-drawn graphics in tutorial classes

This research investigates compression techniques as applied to input from a digitizing tablet. The representations we consider are either drawn from the literature or developed within this thesis; they involve selecting relevant points along the trajectory of the writing pen, and using an interpolating function for reconstruction. The two dimensional parametric polynomial interpolator (e.g linear, quadratic, cubic ) is used for regenerating the trajectory of the pen. Several techniques for selecting relevant points , i.e control points are discussed. We determine our best representation by weighting the criteria, analyzing the experimental results, examining the theoretical considerations and, making where necessary, justifiable tradeoffs. The techniques tested are objectively evaluated in terms of accuracy, efficiency and compactness. The information characteristics (i.e signal entropy) of the handwriting and drawing signals, are estimated from the original and approximated data. Results are discussed and conclusions drawn. The research has been carried out on static data

New Techniques for the Modeling, Processing and Visualization of Surfaces and Volumes

With the advent of powerful 3D acquisition technology, there is a growing demand for the modeling, processing, and visualization of surfaces and volumes. The proposed methods must be efficient and robust, and they must be able to extract the essential structure of the data and to easily and quickly convey the most significant information to a human observer. Independent of the specific nature of the data, the following fundamental problems can be identified: shape reconstruction from discrete samples, data analysis, and data compression. This thesis presents several novel solutions to these problems for surfaces (Part I) and volumes (Part II). For surfaces, we adopt the well-known triangle mesh representation and develop new algorithms for discrete curvature estimation,detection of feature lines, and line-art rendering (Chapter 3), for connectivity encoding (Chapter 4), and for topology preserving compression of 2D vector fields (Chapter 5). For volumes, that are often given as discrete samples, we base our approach for reconstruction and visualization on the use of new trivariate spline spaces on a certain tetrahedral partition. We study the properties of the new spline spaces (Chapter 7) and present efficient algorithms for reconstruction and visualization by iso-surface rendering for both, regularly (Chapter 8) and irregularly (Chapter 9) distributed data samples

Depth-Map Image Compression Based on Region and Contour Modeling

In this thesis, the problem of depth-map image compression is treated. The compilation of articles included in the thesis provides methodological contributions in the fields of lossless and lossy compression of depth-map images.The first group of methods addresses the lossless compression problem. The introduced methods are using the approach of representing the depth-map image in terms of regions and contours. In the depth-map image, a segmentation defines the regions, by grouping pixels having similar properties, and separates them using (region) contours. The depth-map image is encoded by the contours and the auxiliary information needed to reconstruct the depth values in each region.One way of encoding the contours is to describe them using two matrices of horizontal and vertical contour edges. The matrices are encoded using template context coding where each context tree is optimally pruned. In certain contexts, the contour edges are found deterministically using only the currently available information. Another way of encoding the contours is to describe them as a sequence of contour segments. Each such segment is defined by an anchor (starting) point and a string of contour edges, equivalent to a string of chain-code symbols. Here we propose efficient ways to select and encode the anchor points and to generate contour segments by using a contour crossing point analysis and by imposing rules that help in minimizing the number of anchor points.The regions are reconstructed at the decoder using predictive coding or the piecewise constant model representation. In the first approach, the large constant regions are found and one depth value is encoded for each such region. For the rest of the image, suitable regions are generated by constraining the local variation of the depth level from one pixel to another. The nonlinear predictors selected specifically for each region are combining the results of several linear predictors, each fitting optimally a subset of pixels belonging to the local neighborhood. In the second approach, the depth value of a given region is encoded using the depth values of the neighboring regions already encoded. The natural smoothness of the depth variation and the mutual exclusiveness of the values in neighboring regions are exploited to efficiently predict and encode the current region's depth value.The second group of methods is studying the lossy compression problem. In a first contribution, different segmentations are generated by varying the threshold for the depth local variability. A lossy depth-map image is obtained for each segmentation and is encoded based on predictive coding, quantization and context tree coding. In another contribution, the lossy versions of one image are created either by successively merging the constant regions of the original image, or by iteratively splitting the regions of a template image using horizontal or vertical line segments. Merging and splitting decisions are greedily taken, according to the best slope towards the next point in the rate-distortion curve. An entropy coding algorithm is used to encode each image.We propose also a progressive coding method for coding the sequence of lossy versions of a depth-map image. The bitstream is encoded so that any lossy version of the original image is generated, starting from a very low resolution up to lossless reconstruction. The partitions of the lossy versions into regions are assumed to be nested so that a higher resolution image is obtained by splitting some regions of a lower resolution image. A current image in the sequence is encoded using the a priori information from a previously encoded image: the anchor points are encoded relative to the already encoded contour points; the depth information of the newly resulting regions is recovered using the depth value of the parent region.As a final contribution, the dissertation includes a study of the parameterization of planar models. The quantized heights at three-pixel locations are used to compute the optimal plane for each region. The three-pixel locations are selected so that the distortion due to the approximation of the plane over the region is minimized. The planar model and the piecewise constant model are competing in the merging process, where the two regions to be merged are those ensuring the optimal slope in the rate-distortion curve

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

A SENSORY-MOTOR LINGUISTIC FRAMEWORK FOR HUMAN ACTIVITY UNDERSTANDING

We empirically discovered that the space of human actions has a linguistic structure. This is a sensory-motor space consisting of the evolution of joint angles of the human body in movement. The space of human activity has its own phonemes, morphemes, and sentences. We present a Human Activity Language (HAL) for symbolic non-arbitrary representation of sensory and motor information of human activity. This language was learned from large amounts of motion capture data. Kinetology, the phonology of human movement, finds basic primitives for human motion (segmentation) and associates them with symbols (symbolization). This way, kinetology provides a symbolic representation for human movement that allows synthesis, analysis, and symbolic manipulation. We introduce a kinetological system and propose five basic principles on which such a system should be based: compactness, view-invariance, reproducibility, selectivity, and reconstructivity. We demonstrate the kinetological properties of our sensory-motor primitives. Further evaluation is accomplished with experiments on compression and decompression of motion data. The morphology of a human action relates to the inference of essential parts of movement (morpho-kinetology) and its structure (morpho-syntax). To learn morphemes and their structure, we present a grammatical inference methodology and introduce a parallel learning algorithm to induce a grammar system representing a single action. The algorithm infers components of the grammar system as a subset of essential actuators, a CFG grammar for the language of each component representing the motion pattern performed in a single actuator, and synchronization rules modeling coordination among actuators. The syntax of human activities involves the construction of sentences using action morphemes. A sentence may range from a single action morpheme (nuclear syntax) to a sequence of sets of morphemes. A single morpheme is decomposed into analogs of lexical categories: nouns, adjectives, verbs, and adverbs. The sets of morphemes represent simultaneous actions (parallel syntax) and a sequence of movements is related to the concatenation of activities (sequential syntax). We demonstrate this linguistic framework on real motion capture data from a large scale database containing around 200 different actions corresponding to English verbs associated with voluntary meaningful observable movement