Compressing the illumination-adjustable images with principal component analysis.

Pun-Mo Ho.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 90-95).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.2 --- Existing Approaches --- p.2Chapter 1.3 --- Our Approach --- p.3Chapter 1.4 --- Structure of the Thesis --- p.4Chapter 2 --- Related Work --- p.5Chapter 2.1 --- Compression for Navigation --- p.5Chapter 2.1.1 --- Light Field/Lumigraph --- p.5Chapter 2.1.2 --- Surface Light Field --- p.6Chapter 2.1.3 --- Concentric Mosaics --- p.6Chapter 2.1.4 --- On the Compression --- p.7Chapter 2.2 --- Compression for Relighting --- p.7Chapter 2.2.1 --- Previous Approaches --- p.7Chapter 2.2.2 --- Our Approach --- p.8Chapter 3 --- Image-Based Relighting --- p.9Chapter 3.1 --- Plenoptic Illumination Function --- p.9Chapter 3.2 --- Sampling and Relighting --- p.11Chapter 3.3 --- Overview --- p.13Chapter 3.3.1 --- Codec Overview --- p.13Chapter 3.3.2 --- Image Acquisition --- p.15Chapter 3.3.3 --- Experiment Data Sets --- p.16Chapter 4 --- Data Preparation --- p.18Chapter 4.1 --- Block Division --- p.18Chapter 4.2 --- Color Model --- p.23Chapter 4.3 --- Mean Extraction --- p.24Chapter 5 --- Principal Component Analysis --- p.29Chapter 5.1 --- Overview --- p.29Chapter 5.2 --- Singular Value Decomposition --- p.30Chapter 5.3 --- Dimensionality Reduction --- p.34Chapter 5.4 --- Evaluation --- p.37Chapter 6 --- Eigenimage Coding --- p.39Chapter 6.1 --- Transform Coding --- p.39Chapter 6.1.1 --- Discrete Cosine Transform --- p.40Chapter 6.1.2 --- Discrete Wavelet Transform --- p.47Chapter 6.2 --- Evaluation --- p.49Chapter 6.2.1 --- Statistical Evaluation --- p.49Chapter 6.2.2 --- Visual Evaluation --- p.52Chapter 7 --- Relighting Coefficient Coding --- p.57Chapter 7.1 --- Quantization and Bit Allocation --- p.57Chapter 7.2 --- Evaluation --- p.62Chapter 7.2.1 --- Statistical Evaluation --- p.62Chapter 7.2.2 --- Visual Evaluation --- p.62Chapter 8 --- Relighting --- p.65Chapter 8.1 --- Overview --- p.66Chapter 8.2 --- First-Phase Decoding --- p.66Chapter 8.3 --- Second-Phase Decoding --- p.68Chapter 8.3.1 --- Software Relighting --- p.68Chapter 8.3.2 --- Hardware-Assisted Relighting --- p.71Chapter 9 --- Overall Evaluation --- p.81Chapter 9.1 --- Compression of IAIs --- p.81Chapter 9.1.1 --- Statistical Evaluation --- p.81Chapter 9.1.2 --- Visual Evaluation --- p.86Chapter 9.2 --- Hardware-Assisted Relighting --- p.86Chapter 10 --- Conclusion --- p.89Bibliography --- p.9

Spherical mosaic construction using physical analogy for consistent image alignment

The research contained in this thesis is an investigation into mosaic construction. Mosaic techniques are used to obtain images with a large field of view by assembling a sequence of smaller individual overlapping images. In existing methods of mosaic construction only successive images are aligned. Accumulation of small alignment errors occur, and in the case of the image path returning to a previous position in the mosaic, a significant mismatch between nonconsecutive images will result (looping path problem). A new method for consistently aligning all the images in a mosaic is proposed in this thesis. This is achieved by distribution of the small alignment errors. Each image is allowed to modify its position relative to its neighbour images in the mosaic by a small amount with respect to the computed registration. Two images recorded by a rotating ideal camera are related by the same transformation that relates the camera's sensor plane at the time the images were captured. When two images overlap, the intensity values in both images coincide through the intersection line of the sensor planes. This intersection line has the property that the images can be seamlessly joined through that line. An analogy between the images and the physical world is proposed to solve the looping path problem. The images correspond to rigid objects, and these are linked with forces which pull them towards the right positions with respect to their neighbours. That is, every pair of overlapping images are "hinged" through their corresponding intersection line. Aided by another constraint named the spherical constraint, this network of selforganising images has the ability of distributing itself on the surface of a sphere. As a direct result of the new concepts developed in this research work, spherical mosaics (i.e. mosaics with unlimited horizontal and vertical field of view) can be created

Mathematical surfaces models between art and reality

In this paper, I want to document the history of the mathematical surfaces models used for the didactics of pure and applied “High Mathematics” and as art pieces. These models were built between the second half of nineteenth century and the 1930s. I want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore. At the same time the singular beauty of form and colour which the models possessed, aroused the admiration of those entirely ignorant of their mathematical attraction

Visibility computation through image generalization

This dissertation introduces the image generalization paradigm for computing visibility. The paradigm is based on the observation that an image is a powerful tool for computing visibility. An image can be rendered efficiently with the support of graphics hardware and each of the millions of pixels in the image reports a visible geometric primitive. However, the visibility solution computed by a conventional image is far from complete. A conventional image has a uniform sampling rate which can miss visible geometric primitives with a small screen footprint. A conventional image can only find geometric primitives to which there is direct line of sight from the center of projection (i.e. the eye) of the image; therefore, a conventional image cannot compute the set of geometric primitives that become visible as the viewpoint translates, or as time changes in a dynamic dataset. Finally, like any sample-based representation, a conventional image can only confirm that a geometric primitive is visible, but it cannot confirm that a geometric primitive is hidden, as that would require an infinite number of samples to confirm that the primitive is hidden at all of its points. ^ The image generalization paradigm overcomes the visibility computation limitations of conventional images. The paradigm has three elements. (1) Sampling pattern generalization entails adding sampling locations to the image plane where needed to find visible geometric primitives with a small footprint. (2) Visibility sample generalization entails replacing the conventional scalar visibility sample with a higher dimensional sample that records all geometric primitives visible at a sampling location as the viewpoint translates or as time changes in a dynamic dataset; the higher-dimensional visibility sample is computed exactly, by solving visibility event equations, and not through sampling. Another form of visibility sample generalization is to enhance a sample with its trajectory as the geometric primitive it samples moves in a dynamic dataset. (3) Ray geometry generalization redefines a camera ray as the set of 3D points that project at a given image location; this generalization supports rays that are not straight lines, and enables designing cameras with non-linear rays that circumvent occluders to gather samples not visible from a reference viewpoint. ^ The image generalization paradigm has been used to develop visibility algorithms for a variety of datasets, of visibility parameter domains, and of performance-accuracy tradeoff requirements. These include an aggressive from-point visibility algorithm that guarantees finding all geometric primitives with a visible fragment, no matter how small primitive\u27s image footprint, an efficient and robust exact from-point visibility algorithm that iterates between a sample-based and a continuous visibility analysis of the image plane to quickly converge to the exact solution, a from-rectangle visibility algorithm that uses 2D visibility samples to compute a visible set that is exact under viewpoint translation, a flexible pinhole camera that enables local modulations of the sampling rate over the image plane according to an input importance map, an animated depth image that not only stores color and depth per pixel but also a compact representation of pixel sample trajectories, and a curved ray camera that integrates seamlessly multiple viewpoints into a multiperspective image without the viewpoint transition distortion artifacts of prior art methods

Change blindness: eradication of gestalt strategies

Arrays of eight, texture-defined rectangles were used as stimuli in a one-shot change blindness (CB) task where there was a 50% chance that one rectangle would change orientation between two successive presentations separated by an interval. CB was eliminated by cueing the target rectangle in the first stimulus, reduced by cueing in the interval and unaffected by cueing in the second presentation. This supports the idea that a representation was formed that persisted through the interval before being 'overwritten' by the second presentation (Landman et al, 2003 Vision Research 43149–164]. Another possibility is that participants used some kind of grouping or Gestalt strategy. To test this we changed the spatial position of the rectangles in the second presentation by shifting them along imaginary spokes (by ±1 degree) emanating from the central fixation point. There was no significant difference seen in performance between this and the standard task [F(1,4)=2.565, p=0.185]. This may suggest two things: (i) Gestalt grouping is not used as a strategy in these tasks, and (ii) it gives further weight to the argument that objects may be stored and retrieved from a pre-attentional store during this task

Coherent multi-dimensional segmentation of multiview images using a variational framework and applications to image based rendering

Image Based Rendering (IBR) and in particular light field rendering has attracted a lot of attention for interpolating new viewpoints from a set of multiview images. New images of a scene are interpolated directly from nearby available ones, thus enabling a photorealistic rendering. Sampling theory for light fields has shown that exact geometric information in the scene is often unnecessary for rendering new views. Indeed, the band of the function is approximately limited and new views can be rendered using classical interpolation methods. However, IBR using undersampled light fields suffers from aliasing effects and is difficult particularly when the scene has large depth variations and occlusions. In order to deal with these cases, we study two approaches: New sampling schemes have recently emerged that are able to perfectly reconstruct certain classes of parametric signals that are not bandlimited but characterized by a finite number of parameters. In this context, we derive novel sampling schemes for piecewise sinusoidal and polynomial signals. In particular, we show that a piecewise sinusoidal signal with arbitrarily high frequencies can be exactly recovered given certain conditions. These results are applied to parametric multiview data that are not bandlimited. We also focus on the problem of extracting regions (or layers) in multiview images that can be individually rendered free of aliasing. The problem is posed in a multidimensional variational framework using region competition. In extension to previous methods, layers are considered as multi-dimensional hypervolumes. Therefore the segmentation is done jointly over all the images and coherence is imposed throughout the data. However, instead of propagating active hypersurfaces, we derive a semi-parametric methodology that takes into account the constraints imposed by the camera setup and the occlusion ordering. The resulting framework is a global multi-dimensional region competition that is consistent in all the images and efficiently handles occlusions. We show the validity of the approach with captured light fields. Other special effects such as augmented reality and disocclusion of hidden objects are also demonstrated

The benefits of an additional practice in descriptive geomerty course: non obligatory workshop at the Faculty of Civil Engineering in Belgrade

At the Faculty of Civil Engineering in Belgrade, in the Descriptive geometry (DG) course, non-obligatory workshops named “facultative task” are held for the three generations of freshman students with the aim to give students the opportunity to get higher final grade on the exam. The content of this workshop was a creative task, performed by a group of three students, offering free choice of a topic, i.e. the geometric structure associated with some real or imagery architectural/art-work object. After the workshops a questionnaire (composed by the professors at the course) is given to the students, in order to get their response on teaching/learning materials for the DG course and the workshop. During the workshop students performed one of the common tests for testing spatial abilities, named “paper folding". Based on the results of the questionnairethe investigation of the linkages between:students’ final achievements and spatial abilities, as well as students’ expectations of their performance on the exam, and how the students’ capacity to correctly estimate their grades were associated with expected and final grades, is provided. The goal was to give an evidence that a creative work, performed by a small group of students and self-assessment of their performances are a good way of helping students to maintain motivation and to accomplish their achievement. The final conclusion is addressed to the benefits of additional workshops employment in the course, which confirmhigherfinal scores-grades, achievement of creative results (facultative tasks) and confirmation of DG knowledge adaption