A constructive theory of sampling for image synthesis using reproducing kernel bases

Sampling a scene by tracing rays and reconstructing an image from such pointwise samples is fundamental to computer graphics. To improve the efficacy of these computations, we propose an alternative theory of sampling. In contrast to traditional formulations for image synthesis, which appeal to nonconstructive Dirac deltas, our theory employs constructive reproducing kernels for the correspondence between continuous functions and pointwise samples. Conceptually, this allows us to obtain a common mathematical formulation of almost all existing numerical techniques for image synthesis. Practically, it enables novel sampling based numerical techniques designed for light transport that provide considerably improved performance per sample. We exemplify the practical benefits of our formulation with three applications: pointwise transport of color spectra, projection of the light energy density into spherical harmonics, and approximation of the shading equation from a photon map. Experimental results verify the utility of our sampling formulation, with lower numerical error rates and enhanced visual quality compared to existing techniques

Facilitating the design of multidimensional and local transfer functions for volume visualization

The importance of volume visualization is increasing since the sizes of the datasets that need to be inspected grow with every new version of medical scanners (e.g., CT and MR). Direct volume rendering is a 3D visualization technique that has, in many cases, clear benefits over 2D views. It is able to show 3D information, facilitating mental reconstruction of the 3D shape of objects and their spatial relation. The complexity of the settings required in order to generate a 3D rendering is, however, one of the main reasons for this technique not being used more widely in practice. Transfer functions play an important role in the appearance of volume rendered images by determining the optical properties of each piece of the data. The transfer function determines what will be seen and how. The goal of the project on which this PhD thesis reports was to develop and investigate new approaches that would facilitate the setting of transfer functions. As shown in the state of the art overview in Chapter 2, there are two main aspects that influence the effectiveness of a TF: the choice of the TF domain and the process of defining the shape of the TF. The choice of a TF domain, i.e., the choice of the data properties used, directly determines which aspects of the volume data can be visualized. In many approaches, special attention is given to TF domains that would enable an easier selection and visualization of boundaries between materials. The boundaries are an important aspect of the volume data since they reveal the shapes and sizes of objects. Our research in improving the TF definition focused on introducing new user interaction methods and automation techniques that shield the user from the complex process of manually defining the shape and color properties of TFs. Our research dealt with both the TF domain and the TF definition since they are closely related. A suitable TF domain cannot only greatly improve the manual definition, but also, more importantly, increases the possibilities of using automated techniques. Chapter 3 presents a new TF domain. We have used the LH space and the associated LH histogram for TFs based on material boundaries. We showed that the LH space reduces the ambiguity when selecting boundaries compared to the commonly used space of the data value and gradient magnitude. Fur- thermore, boundaries appear as blobs in the LH histogram that make them easier to select. Its compactness and easier selectivity of the boundaries makes the LH histogram suitable for the introduction of clustering-based automation. The mirrored extension of the LH space differentiates between both sides of the boundary. The mirrored LH histogram shows interesting properties of this space, allowing the selection of all boundaries belonging to one material in an easy way. We have also shown that segmentation techniques, such as region growing methods, can benefit from the properties of LH space. Standard cost functions based on the data value and/or the gradient magnitude may experience problems at the boundaries due to the partial volume effect. However, our cost function that is based on the LH space is, however, capable of handling the region growing of boundaries better. Chapter 4 presents an interaction framework for the TF definition based on hierarchical clustering of material boundaries. Our framework aims at an easy combination of various similarity measures that reflect requirements of the user. One of the main benefits of the framework is the absence of similarity-weighting coefficients that are usually hard to define. Further, the framework enables the user to visualize objects that may exist at different levels of the hierarchy. We also introduced two similarity measures that illustrate the functionality of the framework. The main contribution is the first similarity measure that takes advantage of properties of the LH histogram from Chapter 3. We assumed that the shapes of the peaks in the LH histogram can guide the grouping of clusters. The second similarity measure is based on the spatial relationships of clusters. In Chapter 5, we presented part of our research that focused on one of the main issues encountered in the TFs in general. Standard TFs, as they are applied everywhere in the volume in the same way, become difficult to use when the data properties (measurements) of the same material vary over the volume, for example, due to the acquisition inaccuracies. We address this problem by introducing the concept and framework of local transfer functions (LTFs). Local transfer functions are based on using locally applicable TFs in cases where it might be difficult or impossible to define a globally applicable TF. We discussed a number of reasons that hamper the global TF and illustrated how the LTFs may help to alleviate these problems. We have also discussed how multiple TFs can be combined and automatically adapted. One of our contributions is the use of the similarity of local histograms and their correlation for the combination and adaptation of LTFs

Integrating colour correction algorithms

Digital cameras sense colour different than the human visual system (HVS). Digital cameras sense colour using imaging sensor, whereas the HVS senses colour using the cone photoreceptors in our retina. Each digital camera model has its own device specific spectral sensitivity function. It is therefore necessary to convert the device specific colour responses of an imaging sensor to values that are related to the HVS. This process is typically referred to as colour correction, and it is common to the image processing pipeline across all cameras. In this thesis, we explore the topic of colour correction for digital cameras. Colour correction algorithms establish the mapping between device specific responses of the camera with HVS related colour responses. Colour correction algorithms typically need to be trained with datasets. During the training process, we adjust the parameters of the colour correction algorithm, in order to minimise the fitting error between the device specific responses and the corresponding HVS responses. In this thesis, we first show that the choice of the training dataset affects the performance of the colour correction algorithm. Then, we propose to circumvent this problem by considering a reflectance dataset as a set of samples of a much larger reflectance space. We approximate the convex closure of the reflectance dataset in the reflectance space using a hypercube. Finally we integrate over this hypercube in order to calculate a matrix for linear colour correction. By computing the linear colour correction matrix this way, we are able to fill in the gap within a reflectance dataset. We then expand upon the idea of reflectance space further, by allowing all possible reflectances. We explore an alternative formulation of Maximum Ignorance with Positivity (MIP) colour correction. Our alternative formulation allows us to develop a polynomial variant of the concept. Polynomial MIP colour correction is far more complex thant MIP colour correction in terms of formulation. Our contribution is theoretically interesting, however practically, it delivers poorer performance

Aportaciones a la reconstrucción de la reflectancia espectral de una carta de color mediante la captura de imágenes con cámara digital tricromática y distintos iluminantes

Con el propósito de evitar el efecto del metamerismo en la medición de color de los dispositivos de captura de imágenes, se han desarrollado técnicas basadas en el uso de filtros de banda ancha o estrecha acoplados a una cámara digital monocromática de laboratorio para capturar información de color a distintas longitudes de onda y poder realizar la reconstrucción de la reflectancia espectral de la escena basada en un análisis de componentes principales, un análisis de componentes independientes o una matriz de pseudoinversa directa. Lo que no ha quedado cubierto por el estado del arte es la posibilidad de emplear una técnica de reconstrucción basada, no en el uso de filtros, sino en el uso de iluminantes con diferentes temperaturas de color y una cámara doméstica. En el presente trabajo se explora esa posibilidad y se proponen además dos métodos adicionales para la reconstrucción de la reflectancia espectral, basados en el cálculo de las mínimas distancias Euclídeas dentro del espacio Lab entre el parche de color que se desea reconstruir y un subconjunto de parches de color de la carta de entrenamiento.Valle Fayos, JVD. (2015). Aportaciones a la reconstrucción de la reflectancia espectral de una carta de color mediante la captura de imágenes con cámara digital tricromática y distintos iluminantes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48562TESI

異なる空間を繋ぐ光輸送シミュレーション

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 稲葉 雅幸, 東京大学教授 千葉 滋, 東京大学教授 五十嵐 健夫, 東京大学教授 松尾 宇泰, 東京大学講師 中山 英樹, 東京大学講師 蜂須賀 恵也University of Tokyo(東京大学