A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition

In his beautiful book [66], Jean Petitot proposes a sub-Riemannian model for the primary visual cortex of mammals. This model is neurophysiologically justified. Further developments of this theory lead to efficient algorithms for image reconstruction, based upon the consideration of an associated hypoelliptic diffusion. The sub-Riemannian model of Petitot and Citti-Sarti (or certain of its improvements) is a left-invariant structure over the group $SE(2)$ of rototranslations of the plane. Here, we propose a semi-discrete version of this theory, leading to a left-invariant structure over the group $SE(2,N)$, restricting to a finite number of rotations. This apparently very simple group is in fact quite atypical: it is maximally almost periodic, which leads to much simpler harmonic analysis compared to $SE(2).$ Based upon this semi-discrete model, we improve on previous image-reconstruction algorithms and we develop a pattern-recognition theory that leads also to very efficient algorithms in practice.Comment: 123 pages, revised versio

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

MAGNETIC RESONANCE ELASTOGRAPHY FOR APPLICATIONS IN RADIATION THERAPY

Magnetic resonance elastography (MRE) is an imaging technique that combines mechanical waves and magnetic resonance imaging (MRI) to determine the elastic properties of tissue. Because MRE is non-invasive, there is great potential and interest for its use in the detection of cancer. The first part of this thesis concentrates on parameter optimization and imaging quality of an MRE system. To do this, we developed a customized quality assurance phantom, and a series of quality control tests to characterize the MRE system. Our results demonstrated that through optimizing scan parameters, such as frequency and amplitude, MRE could provide a good qualitative elastogram for targets with different elasticity values and dimensions. The second part investigated the feasibility of integrating MRE into radiation therapy (RT) workflow. With the aid of a tissue-equivalent prostate phantom (embedded with three dominant intraprostatic lesions (DILs)), an MRE-integrated RT framework was developed. This framework contains a comprehensive scan protocol including Computed Tomography (CT) scan, combined MRI/MRE scans and a Volumetric Modulated Arc Therapy (VMAT) technique for treatment delivery. The results showed that using the comprehensive information could boost the MRE defined DILs to 84 Gy while keeping the remainder of the prostate to 78 Gy. Using a VMAT based technique allowed us to achieve a highly conformal plan (conformity index for the prostate and combined DILs was 0.98 and 0.91). Based on our feasibility study, we concluded that MRE data can be used for targeted radiation dose escalation. In summary, this thesis demonstrates that MRE is feasible for applications in radiation oncology

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Real-time hand gesture recognition exploiting multiple 2D and 3D cues

The recent introduction of several 3D applications and stereoscopic display technologies has created the necessity of novel human-machine interfaces. The traditional input devices, such as keyboard and mouse, are not able to fully exploit the potential of these interfaces and do not offer a natural interaction. Hand gestures provide, instead, a more natural and sometimes safer way of interacting with computers and other machines without touching them. The use cases for gesture-based interfaces range from gaming to automatic sign language interpretation, health care, robotics, and vehicle automation. Automatic gesture recognition is a challenging problem that has been attaining a growing interest in the research field for several years due to its applications in natural interfaces. The first approaches, based on the recognition from 2D color pictures or video only, suffered of the typical problems characterizing such type of data. Inter occlusions, different skin colors among users even of the same ethnic group and unstable illumination conditions, in facts, often made this problem intractable. Other approaches, instead, solved the previous problems by making the user wear sensorized gloves or hold proper tools designed to help the hand localization in the scene. The recent introduction in the mass market of novel low-cost range cameras, like the Microsoft Kinect, Asus XTION, Creative Senz3D, and the Leap Motion, has opened the way to innovative gesture recognition approaches exploiting the geometry of the framed scene. Most methods share a common gesture recognition pipeline based on firstly identifying the hand in the framed scene, then extracting some relevant features on the hand samples and finally exploiting suitable machine learning techniques in order to recognize the performed gesture from a predefined ``gesture dictionary''. This thesis, based on the previous rationale, proposes a novel gesture recognition framework exploiting both color and geometric cues from low-cost color and range cameras. The dissertation starts by introducing the automatic hand gesture recognition problem, giving an overview of the state-of-art algorithms and the recognition pipeline employed in this work. Then, it briefly describes the major low-cost range cameras and setups used in literature for color and depth data acquisition for hand gesture recognition purposes, highlighting their capabilities and limitations. The methods employed for respectively detecting the hand in the framed scene and segmenting it in its relevant parts are then analyzed with a higher level of detail. The algorithm first exploits skin color information and geometrical considerations for discarding the background samples, then it reliably detects the palm and the finger regions, and removes the forearm. For the palm detection, the method fits the largest circle inscribed in the palm region or, in a more advanced version, an ellipse. A set of robust color and geometric features which can be extracted from the fingers and palm regions, previously segmented, is then illustrated accurately. Geometric features describe properties of the hand contour from its curvature variations, the distances in the 3D space or in the image plane of its points from the hand center or from the palm, or extract relevant information from the palm morphology and from the empty space in the hand convex hull. Color features exploit, instead, the histogram of oriented gradients (HOG), local phase quantization (LPQ) and local ternary patterns (LTP) algorithms to provide further helpful cues from the hand texture and the depth map treated as a grayscale image. Additional features extracted from the Leap Motion data complete the gesture characterization for a more reliable recognition. Moreover, the thesis also reports a novel approach jointly exploiting the geometric data provided by the Leap Motion and the depth data from a range camera for extracting the same depth features with a significantly lower computational effort. This work then addresses the delicate problem of constructing a robust gesture recognition model from the features previously described, using multi-class Support Vector Machines, Random Forests or more powerful ensembles of classifiers. Feature selection techniques, designed to detect the smallest subset of features that allow to train a leaner classification model without a significant accuracy loss, are also considered. The proposed recognition method, tested on subsets of the American Sign Language and experimentally validated, reported very high accuracies. The results showed also how higher accuracies are obtainable by combining proper sets of complementary features and using ensembles of classifiers. Moreover, it is worth noticing that the proposed approach is not sensor dependent, that is, the recognition algorithm is not bound to a specific sensor or technology adopted for the depth data acquisition. Eventually, the gesture recognition algorithm is able to run in real-time even in absence of a thorough optimization, and may be easily extended in a near future with novel descriptors and the support for dynamic gestures

Functional and structural MRI image analysis for brain glial tumors treatment

This Ph.D Thesis is the outcome of a close collaboration between the Center for Research in Image Analysis and Medical Informatics (CRAIIM) of the Insubria University and the Operative Unit of Neurosurgery, Neuroradiology and Health Physics of the University Hospital ”Circolo Fondazione Macchi”, Varese. The project aim is to investigate new methodologies by means of whose, develop an integrated framework able to enhance the use of Magnetic Resonance Images, in order to support clinical experts in the treatment of patients with brain Glial tumor. Both the most common uses of MRI technology for non-invasive brain inspection were analyzed. From the Functional point of view, the goal has been to provide tools for an objective reliable and non-presumptive assessment of the brain’s areas locations, to preserve them as much as possible at surgery. From the Structural point of view, methodologies for fully automatic brain segmentation and recognition of the tumoral areas, for evaluating the tumor volume, the spatial distribution and to be able to infer correlation with other clinical data or trace growth trend, have been studied. Each of the proposed methods has been thoroughly assessed both qualitatively and quantitatively. All the Medical Imaging and Pattern Recognition algorithmic solutions studied for this Ph.D. Thesis have been integrated in GliCInE: Glioma Computerized Inspection Environment, which is a MATLAB prototype of an integrated analysis environment that offers, in addition to all the functionality specifically described in this Thesis, a set of tools needed to manage Functional and Structural Magnetic Resonance Volumes and ancillary data related to the acquisition and the patient