TY - BOOK

T1 - On Texture and Geometry in Image Analysis

AU - Gustafsson, David Karl John

PY - 2009

Y1 - 2009

N2 - Images are composed of geometric structure and texture. Large scale structuresare considered to be the geometric structure, while small scale detailsare considered to be the texture. In this dissertation, we will argue that themost important difference between geometric structure and texture is notthe scale - instead, it is the requirement on representation or reconstruction.Geometric structure must be reconstructed exactly and can be representedsparsely. Texture does not need to be reconstructed exactly, a random samplefrom the distribution being sufficient. Furthermore, texture can not berepresented sparsely.In image inpainting, the image content is missing in a region and shouldbe reconstructed using information from the rest of the image. The mainchallenges in inpainting are: prolonging and connecting geometric structureand reproducing the variation found in texture. The Filter, Random fieldsand Maximum Entropy (FRAME) model [213, 214] is used for inpaining texture.We argue that many ’textures’ contain details that must be inpaintedexactly. Simultaneous reconstruction of geometric structure and texture isa difficult problem, therefore, a two-phase reconstruction procedure is proposed.An inverse temperature is added to the FRAME model. In the firstphase, the geometric structure is reconstructed by cooling the distribution,and in the second phase, the texture is added by heating the distribution.Empirically, we show that the long range geometric structure is inpainted ina visually appealing way during the first phase, and texture is added in thesecond phase by heating the distribution.A method for measuring and quantifying the image content in terms ofgeometric structure and texture is proposed. It is assumed that geometricstructures can be represented sparsely, while texture can not. Reversingthe argumentation, we argue that if the image can be represented sparselythen it contains mainly geometric structure, and if it cannot be representedsparsely then it contains texture. The degree of geometric structure is determinedby the sparseness of the representation. A Truncated Singular ValueDecomposition complexity measure is proposed, where the rank of a goodapproximation is defining the image complexity.Image regularization can be viewed as approximating an observed imagewith a simpler image. The property of the simpler image depends on the regularizationmethod, a regularization parameter and the image content. Herewe analyze the norm of the regularized solution and the norm of the residualas a function of the regularization parameter (using different regularizationmethods). The aim is to characterize the image content by the content in theresidual. Buades et al. [27] used the content in the residual - called ’Method Noise’ - for evaluating denoising methods. Our aim is complementary, as wewant to characterize the image content in terms of geometric structure andtexture, using different regularization methods.The image content does not depend solely on the objects in the scene, butalso on the viewing distance. Increasing the viewing distance influences theimage content in two different ways. As the viewing distance increases, detailsare suppressed because the inner scale also increases. By increasing theviewing distance, the spatial lay-out of the captured scene will also change.At large viewing distances, the sky occupies a large region in the imageand buildings, trees and lawns appear as uniformly colored regions. Thefollowing questions are addressed: How much of the visual appearance interms of geometry and texture of an image can be explained by the classicalresults from natural image statistics? and how does the visual appearanceof an image and the classical statistics relate to the viewing distance?

AB - Images are composed of geometric structure and texture. Large scale structuresare considered to be the geometric structure, while small scale detailsare considered to be the texture. In this dissertation, we will argue that themost important difference between geometric structure and texture is notthe scale - instead, it is the requirement on representation or reconstruction.Geometric structure must be reconstructed exactly and can be representedsparsely. Texture does not need to be reconstructed exactly, a random samplefrom the distribution being sufficient. Furthermore, texture can not berepresented sparsely.In image inpainting, the image content is missing in a region and shouldbe reconstructed using information from the rest of the image. The mainchallenges in inpainting are: prolonging and connecting geometric structureand reproducing the variation found in texture. The Filter, Random fieldsand Maximum Entropy (FRAME) model [213, 214] is used for inpaining texture.We argue that many ’textures’ contain details that must be inpaintedexactly. Simultaneous reconstruction of geometric structure and texture isa difficult problem, therefore, a two-phase reconstruction procedure is proposed.An inverse temperature is added to the FRAME model. In the firstphase, the geometric structure is reconstructed by cooling the distribution,and in the second phase, the texture is added by heating the distribution.Empirically, we show that the long range geometric structure is inpainted ina visually appealing way during the first phase, and texture is added in thesecond phase by heating the distribution.A method for measuring and quantifying the image content in terms ofgeometric structure and texture is proposed. It is assumed that geometricstructures can be represented sparsely, while texture can not. Reversingthe argumentation, we argue that if the image can be represented sparselythen it contains mainly geometric structure, and if it cannot be representedsparsely then it contains texture. The degree of geometric structure is determinedby the sparseness of the representation. A Truncated Singular ValueDecomposition complexity measure is proposed, where the rank of a goodapproximation is defining the image complexity.Image regularization can be viewed as approximating an observed imagewith a simpler image. The property of the simpler image depends on the regularizationmethod, a regularization parameter and the image content. Herewe analyze the norm of the regularized solution and the norm of the residualas a function of the regularization parameter (using different regularizationmethods). The aim is to characterize the image content by the content in theresidual. Buades et al. [27] used the content in the residual - called ’Method Noise’ - for evaluating denoising methods. Our aim is complementary, as wewant to characterize the image content in terms of geometric structure andtexture, using different regularization methods.The image content does not depend solely on the objects in the scene, butalso on the viewing distance. Increasing the viewing distance influences theimage content in two different ways. As the viewing distance increases, detailsare suppressed because the inner scale also increases. By increasing theviewing distance, the spatial lay-out of the captured scene will also change.At large viewing distances, the sky occupies a large region in the imageand buildings, trees and lawns appear as uniformly colored regions. Thefollowing questions are addressed: How much of the visual appearance interms of geometry and texture of an image can be explained by the classicalresults from natural image statistics? and how does the visual appearanceof an image and the classical statistics relate to the viewing distance?

KW - Faculty of Science

M3 - Ph.D. thesis

BT - On Texture and Geometry in Image Analysis

CY - Datalogisk Institut, Københavns Universitet

ER -