This thesis addresses a number of problems in computer vision, image processing, and geometry processing, and presents novel solutions to these problems. The overarching theme of the techniques presented here is a multi-scale approach, leveraging mathematical tools to represent images and surfaces at different scales, and methods that can be adapted from one type of domain (eg., the plane) to another (eg., the sphere). The main problem addressed in this thesis is known as stereo reconstruction: reconstructing the geometry of a scene or object from two or more images of that scene. We develop novel algorithms to do this, which work for both planar and spherical images. By developing a novel way to formulate the notion of disparity for spherical images, we are able effectively adapt our algorithms from planar to spherical images. Our stereo reconstruction algorithm is based on a novel application of distance transforms to multi-scale matching. We use matching information aggregated over multiple scales, and enforce consistency between these scales using distance transforms. We then show how multiple spherical disparity maps can be efficiently and robustly fused using visibility and other geometric constraints. We then show how the reconstructed point clouds can be used to synthesize a realistic sequence of novel views, images from points of view not captured in the input images, in real-time. Along the way to this result, we address some related problems. For example, multi-scale features can be detected in spherical images by convolving those images with a filterbank, generating an overcomplete spherical wavelet representation of the image from which the multiscale features can be extracted. Convolution of spherical images is much more efficient in the spherical harmonic domain than in the spatial domain. Thus, we develop a GPU implementation for fast spherical harmonic transforms and frequency domain convolutions of spherical images. This tool can also be used to detect multi-scale features on geometric surfaces. When we have a point cloud of a surface of a particular class of object, whether generated by stereo reconstruction or by some other modality, we can use statistics and machine learning to more robustly estimate the surface. If we have at our disposal a database of surfaces of a particular type of object, such as the human face, we can compute statistics over this database to constrain the possible shape a new surface of this type can take. We show how a statistical spherical wavelet shape prior can be used to efficiently and robustly reconstruct a face shape from noisy point cloud data, including stereo data.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20377号 / 工博第4314号 / 新制||工||1668(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 篠原 真毅, 教授 和田 修己, 教授 大村 善治 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

No description available.

El silicio es un material de suma importancia en microelectronica y en fotonica. Las propiedades semiconductoras del silicio estan detras de los conceptos que gobiernan el funcionamiento de la mayoría de los dispositivos electronicos como los diodos y los transistores. El concepto de integracion ha permitido procesar dispositivos muy pequeños, llegando a alcanzar un tamaño nanometrico. El alto indice de refraccion del silicio permite confinar la luz en estructuras de tamaño micrometrico. Este es el caso de dispositivos fotonicos tales como las guias de onda y las cavidades. Usualmente, tanto los dispositivos fotonicos como los electronicos estan basados en la tecnologia planar, es decir poseen una topologia plana, siendo esto una fuente de perdidas. Es bien conocido que las cavidades esfericas confinan la luz con mas eficiencia que las cavidades planares. Esta tesis trata sobre el desarrollo de un nuevo tipo de microparticulas esfericas que llamamos Coloides de Silicio. Debido a su forma esferica, su alto indice de refraccion y su suave superficie, estas particulas funcionan como microcavidades opticas con modos resonantes bien definidos en el infrarrojo cercano. La tesis reporta sobre la sintesis, y las propiedades estructurales y opticas de los coloides de silicio con diametro entre 0.5 y 3.5 micrometros. Los coloides de silicio pueden facilitar el desarrollo de microcavidades de alto factor de calidad con alta eficiencia de confinamiento de la luz, y permitir la integracion de dispositivos electronicos y fotonicos tales como una union p-n en una sola particula coloidal. Esta tesis reporta tambien sobre los coloides de silicio como elementos integrantes de las Esponjas Fotonicas, las cuales estan formadas por una red desordenada de microesferas de silicio de diferentes tamaños, e interaccionan con la luz fuertemente en un ancho rango de longitudes de onda. / Tymczenko, MK. (2010). Photonic microcavities and photonic sponges based on silicon colloids [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8425

The Funk–Radon transform assigns to a function on the two-sphere its mean values along all great circles. We consider the following generalization: we replace the great circles by the small circles being the intersection of the sphere with planes containing a common point ζ inside the sphere. If ζ is the origin, this is just the classical Funk–Radon transform. We find two mappings from the sphere to itself that enable us to represent the generalized Radon transform in terms of the Funk–Radon transform. This representation is utilized to characterize the nullspace and range as well as to prove an inversion formula of the generalized Radon transform.

<p>Fans are often used in equipment such as home appliances andelectronic equipment where the margin of profit is small butcustomers demands on a low noise level are high. Therefore,methods for predicting the noise emitted by an applicationincluding one or several fans are desirable in order toimprove, accelerate and reduce the cost of low-noise design.The Noise Shaping Technology (NST) has been developed withinthe EC-project NABUCCO in order to fulfil the aboverequirements on a prediction method. According to NST, thenoise source (not necessary a fan) is described by one orseveral noise descriptors, CSSs, and the correspondingtransmission paths through the structure described by one orseveral transfer functions, ACFs. In this thesis, theapplicability of NST is evaluated on a cabinet for electronicequipment where small axial cooling fans constitute the primarysources of the airborne sound.</p><p>As an axial fan is a complex source of sound,simplifications are necessary when modelling its acousticproperties. Therefore, the sound radiation of an axial fan infree space was examined by expanding the generated soundpressure field into spherical harmonics. The conclusion on asource model for the cabinet example, where the fans are moreor less In-duct mounted, is a modified single axial dipole. Themodel is expected to be valid in the entire frequency range ofinterest except in the mid-frequency range where the modaldensity is low. In order to improve the source model in thisfrequency range, a future model based on a rotating dipole isproposed.</p><p>The sound power of a small axial fan is measured in an ISO10302 test-rig. In order to take account of flow conditions,acoustically transparent ducts have been developed. These shallbe attached to the test-rig when measuring the sound power ofthe fan. A simple but practical method of how to correct thesound power for the baffling effect of the test-rig has alsobeen developed. Finally, the sound power can be converted intodipole force, which is the airborne CSS corresponding to thesingle axial dipole model.</p><p>The corresponding airborne transfer function (ACF), i.e.,from dipole force at the source point to sound pressure at thereceiver point, is measured reciprocally by taking use ofLyamshevs reciprocity relation.</p><p>From multiplication of the CSS and the ACF, the soundpressure can be predicted. The prediction shows quite goodagreement with the measured values.</p><p><b>Keywords:</b>axial fan, airborne sound, sourcecharacterisation, transmission path analysis, In-duct,spherical harmonics, rotating dipole, installation effects, ISO10302, flow conditions, baffling effect, acousticallytransparent ducts, Lyamshevs reciprocity relation, reciprocity,CSS, ACF, GSM, NST.</p>

We are interested in the onset of instability of the axisymmetric flow between two concentric spherical shells that differentially rotate about a common axis in the narrow-gap limit. The expected mode of instability takes the form of roughly square axisymmetric Taylor vortices which arise in the vicinity of the equator and are modulated on a latitudinal length scale large compared to the gap width but small compared to the shell radii. At the heart of the difficulties faced is the presence of phase mixing in the system, characterised by a non-zero frequency gradient at the equator and the tendency for vortices located off the equator to oscillate. This mechanism serves to enhance viscous dissipation in the fluid with the effect that the amplitude of any initial disturbance generated at onset is ultimately driven to zero. In this thesis we study a complex Ginzburg-Landau equation derived from the weakly nonlinear analysis of Harris, Bassom and Soward [D. Harris, A. P. Bassom, A. M. Soward, Global bifurcation to travelling waves with application to narrow gap spherical Couette flow, Physica D 177 (2003) p. 122-174] (referred to as HBS) to govern the amplitude modulation of Taylor vortex disturbances in the vicinity of the equator. This equation was developed in a regime that requires the angular velocities of the bounding spheres to be very close. When the spherical shells do not co-rotate, it has the remarkable property that the linearised form of the equation has no non-trivial neutral modes. Furthermore no steady solutions to the nonlinear equation have been found. Despite these challenges Bassom and Soward [A. P. Bassom, A. M. Soward, On finite amplitude subcritical instability in narrow-gap spherical Couette flow, J. Fluid Mech. 499 (2004) p. 277-314] (referred to as BS) identified solutions to the equation in the form of pulse-trains. These pulse-trains consist of oscillatory finite amplitude solutions expressed in terms of a single complex amplitude localised as a pulse about the origin. Each pulse oscillates at a frequency proportional to its distance from the equatorial plane and the whole pulse-train is modulated under an envelope and drifts away from the equator at a relatively slow speed. The survival of the pulse-train depends upon the nonlinear mutual-interaction of close neighbours; as the absence of steady solutions suggests, self-interaction is inadequate. Though we report new solutions to the HBS co-rotation model the primary focus in this work is the physically more interesting case when the shell velocities are far from close. More specifically we concentrate on the investigation of BS-style pulse-train solutions and, in the first part of this thesis, develop a generic framework for the identification and classification of pulse-train solutions. Motivated by relaxation oscillations identified by Cole [S. J. Cole, Nonlinear rapidly rotating spherical convection, Ph.D. thesis, University of Exeter (2004)] whilst studying the related problem of thermal convection in a rapidly rotating self-gravitating sphere, we extend the HBS equation in the second part of this work. A model system is developed which captures many of the essential features exhibited by Cole's, much more complicated, system of equations. We successfully reproduce relaxation oscillations in this extended HBS model and document the solution as it undergoes a series of interesting bifurcations.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

We present a system that estimates the motion of a robot relying solely on images from onboard omnidirectional camera (visual odometry). Compared to other visual odometry hardware, ours is unusual in utilizing high resolution, low frame-rate (1 to 3 Hz) omnidirectional camera mounted on a robot that is propelled using continuous tracks. We focus on high precision estimates in scenes, where objects are far away from the camera. This is achieved by utilizing omnidirectional camera that is able to stabilize the motion estimates between camera frames that are known to be ill-conditioned for narrow field of view cameras. We employ feature based-approach for estimation camera motion. Given our hardware, possibly high ammounts of camera rotation between frames can occur. Thus we use techniques of feature matching rather than feature tracking.

We present a system that estimates the motion of a robot relying solely on images from onboard omnidirectional camera (visual odometry). Compared to other visual odometry hardware, ours is unusual in utilizing high resolution, low frame-rate (1 to 3 Hz) omnidirectional camera mounted on a robot that is propelled using continuous tracks. We focus on high precision estimates in scenes, where objects are far away from the camera. This is achieved by utilizing omnidirectional camera that is able to stabilize the motion estimates between camera frames that are known to be ill-conditioned for narrow field of view cameras. We employ feature based-approach for estimation camera motion. Given our hardware, possibly high ammounts of camera rotation between frames can occur. Thus we use techniques of feature matching rather than feature tracking.