High-Quality Image Resizing Using Oblique Projection Operators

The standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate. However, one can obtain more accurate results if one applies a filter prior to sampling, a fact well known from sampling theory. The optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space. Unfortunately, the optimal projection prefilter is difficult to implement when sinc or high order spline functions are used. In this paper, we propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster, simpler, and more general algorithms. We show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space. The main advantage is that it becomes perfectly feasible to use higher order models (e.g., splines of degree n ≥ 3). We develop the theoretical background and present a simple and practical implementation procedure using B-splines. Our experiments show that the proposed algorithm consistently outperforms the standard interpolation methods and that it provides essentially the same performance as the optimal procedure (least squares solution) with considerably fewer computations. The method works for arbitrary scaling factors and is applicable to both image enlargement and reduction

Least-Squares Image Resizing Using Finite Differences

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree n. A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a. For a given choice of basis functions, the results of our method are consistently better than those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal-to-noise ratio. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivatives

Nondyadic and nonlinear multiresolution image approximations

This thesis focuses on the development of novel multiresolution image approximations. Specifically, we present two kinds of generalization of multiresolution techniques: image reduction for arbitrary scales, and nonlinear approximations using other metrics than the standard Euclidean one. Traditional multiresolution decompositions are restricted to dyadic scales. As first contribution of this thesis, we develop a method that goes beyond this restriction and that is well suited to arbitrary scale-change computations. The key component is a new and numerically exact algorithm for computing inner products between a continuously defined signal and B-splines of any order and of arbitrary sizes. The technique can also be applied for non-uniform to uniform grid conversion, which is another approximation problem where our method excels. Main applications are resampling and signal reconstruction. Although simple to implement, least-squares approximations lead to artifacts that could be reduced if nonlinear methods would be used instead. The second contribution of the thesis is the development of nonlinear spline pyramids that are optimal for lp-norms. First, we introduce a Banach-space formulation of the problem and show that the solution is well defined. Second, we compute the lp-approximation thanks to an iterative optimization algorithm based on digital filtering. We conclude that l1-approximations reduce the artifacts that are inherent to least-squares methods; in particular, edge blurring and ringing. In addition, we observe that the error of l1-approximations is sparser. Finally, we derive an exact formula for the asymptotic Lp-error; this result justifies using the least-squares approximation as initial solution for the iterative optimization algorithm when the degree of the spline is even; otherwise, one has to include an appropriate correction term. The theoretical background of the thesis includes the modelisation of images in a continuous/discrete formalism and takes advantage of the approximation theory of linear shift-invariant operators. We have chosen B-splines as basis functions because of their nice properties. We also propose a new graphical formalism that links B-splines, finite differences, differential operators, and arbitrary scale changes

Projection and interpolation based techniques for structured and impulsive noise filtering

In this chapter we present the relevant mathematical background to address two well defined signal and image processing problems. Namely, the problem of structured noise filtering and the problem of interpolation of missing data. The former is addressed by recourse to oblique projection based techniques whilst the latter, which can be considered equivalent to impulsive noise filtering, is tackled by appropriate interpolation methods

High-Quality Parallel-Ray x-Ray CT Back Projection Using Optimized Interpolation

We propose a new, cost-efficient method for computing back projections in parallel-ray X-ray CT. Forward and back projections are the basis of almost all X-ray CT reconstruction methods, but computing these accurately is costly. In the special case of parallel-ray geometry, it turns out that reconstruction requires back projection only. One approach to accelerate the back projection is through interpolation: fit a continuous representation to samples of the desired signal, then sample it at the required locations. Instead, we propose applying a prefilter that has the effect of orthogonally projecting the underlying signal onto the space spanned by the interpolator, which can significantly improve the quality of the interpolation. We then build on this idea by using oblique projection, which simplifies the computation while giving effectively the same improvement in quality. Our experiments on analytical phantoms show that this refinement can improve the reconstruction quality for both filtered back projection and iterative reconstruction in the high-quality regime, i.e., with low noise and many measurements

Automated Pattern Detection and Generalization of Building Groups

This dissertation focuses on the topic of building group generalization by considering the detection of building patterns. Generalization is an important research field in cartography, which is part of map production and the basis for the derivation of multiple representation. As one of the most important features on map, buildings occupy large amount of map space and normally have complex shape and spatial distribution, which leads to that the generalization of buildings has long been an important and challenging task. For social, architectural and geographical reasons, the buildings were built with some special rules which forms different building patterns. Building patterns are crucial structures which should be carefully considered during graphical representation and generalization. Although people can effortlessly perceive these patterns, however, building patterns are not explicitly described in building datasets. Therefore, to better support the subsequent generalization process, it is important to automatically recognize building patterns. The objective of this dissertation is to develop effective methods to detect building patterns from building groups. Based on the identified patterns, some generalization methods are proposed to fulfill the task of building generalization. The main contribution of the dissertation is described as the following five aspects: (1) The terminology and concept of building pattern has been clearly explained; a detailed and relative complete typology of building patterns has been proposed by summarizing the previous researches as well as extending by the author; (2) A stroke-mesh based method has been developed to group buildings and detect different patterns from the building groups; (3) Through the analogy between line simplification and linear building group typification, a stroke simplification based typification method has been developed aiming at solving the generalization of building groups with linear patterns; (4) A mesh-based typification method has been developed for the generalization of the building groups with grid patterns; (5) A method of extracting hierarchical skeleton structures from discrete buildings have been proposed. The extracted hierarchical skeleton structures are regarded as the representations of the global shape of the entire region, which is used to control the generalization process. With the above methods, the building patterns are detected from the building groups and the generalization of building groups are executed based on the patterns. In addition, the thesis has also discussed the drawbacks of the methods and gave the potential solutions.:Abstract I Kurzfassung III Contents V List of Figures IX List of Tables XIII List of Abbreviations XIV Chapter 1 Introduction 1 1.1 Background and motivation 1 1.1.1 Cartographic generalization 1 1.1.2 Urban building and building patterns 1 1.1.3 Building generalization 3 1.1.4 Hierarchical property in geographical objects 3 1.2 Research objectives 4 1.3 Study area 5 1.4 Thesis structure 6 Chapter 2 State of the Art 8 2.1 Operators for building generalization 8 2.1.1 Selection 9 2.1.2 Aggregation 9 2.1.3 Simplification 10 2.1.4 Displacement 10 2.2 Researches of building grouping and pattern detection 11 2.2.1 Building grouping 11 2.2.2 Pattern detection 12 2.2.3 Problem analysis . 14 2.3 Researches of building typification 14 2.3.1 Global typification 15 2.3.2 Local typification 15 2.3.3 Comparison analysis 16 2.3.4 Problem analysis 17 2.4 Summary 17 Chapter 3 Using stroke and mesh to recognize building group patterns 18 3.1 Abstract 19 3.2 Introduction 19 3.3 Literature review 20 3.4 Building pattern typology and study area 22 3.4.1 Building pattern typology 22 3.4.2 Study area 24 3.5 Methodology 25 3.5.1 Generating and refining proximity graph 25 3.5.2 Generating stroke and mesh 29 3.5.3 Building pattern recognition 31 3.6 Experiments 33 3.6.1 Data derivation and test framework 33 3.6.2 Pattern recognition results 35 3.6.3 Evaluation 39 3.7 Discussion 40 3.7.1 Adaptation of parameters 40 3.7.2 Ambiguity of building patterns 44 3.7.3 Advantage and Limitation 45 3.8 Conclusion 46 Chapter 4 A typification method for linear building groups based on stroke simplification 47 4.1 Abstract 48 4.2 Introduction 48 4.3 Detection of linear building groups 50 4.3.1 Stroke-based detection method 50 4.3.2 Distinguishing collinear and curvilinear patterns 53 4.4 Typification method 55 4.4.1 Analogy of building typification and line simplification 55 4.4.2 Stroke generation 56 4.4.3 Stroke simplification 57 4.5 Representation of newly typified buildings 60 4.6 Experiment 63 4.6.1 Linear building group detection 63 4.6.2 Typification results 65 4.7 Discussion 66 4.7.1 Comparison of reallocating remained nodes 66 4.7.2 Comparison with classic line simplification method 67 4.7.3 Advantage 69 4.7.4 Further improvement 71 4.8 Conclusion 71 Chapter 5 A mesh-based typification method for building groups with grid patterns 73 5.1 Abstract 74 5.2 Introduction 74 5.3 Related work 75 5.4 Methodology of mesh-based typification 78 5.4.1 Grid pattern classification 78 5.4.2 Mesh generation 79 5.4.3 Triangular mesh elimination 80 5.4.4 Number and positioning of typified buildings 82 5.4.5 Representation of typified buildings 83 5.4.6 Resizing Newly Typified Buildings 85 5.5 Experiments 86 5.5.1 Data derivation 86 5.5.2 Typification results and evaluation 87 5.5.3 Comparison with official map 91 5.6 Discussion 92 5.6.1 Advantages 92 5.6.2 Further improvements 93 5.7 Conclusion 94 Chapter 6 Hierarchical extraction of skeleton structures from discrete buildings 95 6.1 Abstract 96 6.2 Introduction 96 6.3 Related work 97 6.4 Study area 99 6.5 Hierarchical extraction of skeleton structures 100 6.5.1 Proximity Graph Network (PGN) of buildings 100 6.5.2 Centrality analysis of proximity graph network 103 6.5.3 Hierarchical skeleton structures of buildings 108 6.6 Generalization application 111 6.7 Experiment and discussion 114 6.7.1 Data statement 114 6.7.2 Experimental results 115 6.7.3 Discussion 118 6.8 Conclusions 120 Chapter 7 Discussion 121 7.1 Revisiting the research problems 121 7.2 Evaluation of the presented methodology 123 7.2.1 Strengths 123 7.2.2 Limitations 125 Chapter 8 Conclusions 127 8.1 Main contributions 127 8.2 Outlook 128 8.3 Final thoughts 131 Bibliography 132 Acknowledgements 142 Publications 14

Notions of symmetry in human movement for recognition

Notions of symmetry are powerful for understanding as they explore relationships in nature for analysis. We describe how symmetry analysis can be used to recognize people by their gait. This approachis reinforced by the view from psychology that human gait is a symmetrical pattern of motion and that symmetrical properties of human movement can indeed be used for human gait analysis.Here, we use gait as a vehicle to investigate both the symmetry of moving objects as provided in our new spatial and spatio-temporal symmetry analyses. We apply these symmetry extractions to a numberof databases to demonstrate their potency. A performance analysis shows that using symmetry for gait recognition enjoys practical advantages such as relative immunity to noise, ability to handlemissing information and the capability to handle occlusion. The results show that the symmetrical properties of human gait appear to be unique and can indeed be used for analysis and for recognition with recognition rates exceeding 90%. Best performance is achieved by a spatio-temporal operator, reflecting the view that recognition by gait is not just from body shape, but also by the way the body moves

Robust Single-view Cone-beam X-ray Pose Estimation with Neural Tuned Tomography (NeTT) and Masked Neural Radiance Fields (mNeRF)

Many tasks performed in image-guided, mini-invasive, medical procedures can be cast as pose estimation problems, where an X-ray projection is utilized to reach a target in 3D space. Expanding on recent advances in the differentiable rendering of optically reflective materials, we introduce new methods for pose estimation of radiolucent objects using X-ray projections, and we demonstrate the critical role of optimal view synthesis in performing this task. We first develop an algorithm (DiffDRR) that efficiently computes Digitally Reconstructed Radiographs (DRRs) and leverages automatic differentiation within TensorFlow. Pose estimation is performed by iterative gradient descent using a loss function that quantifies the similarity of the DRR synthesized from a randomly initialized pose and the true fluoroscopic image at the target pose. We propose two novel methods for high-fidelity view synthesis, Neural Tuned Tomography (NeTT) and masked Neural Radiance Fields (mNeRF). Both methods rely on classic Cone-Beam Computerized Tomography (CBCT); NeTT directly optimizes the CBCT densities, while the non-zero values of mNeRF are constrained by a 3D mask of the anatomic region segmented from CBCT. We demonstrate that both NeTT and mNeRF distinctly improve pose estimation within our framework. By defining a successful pose estimate to be a 3D angle error of less than 3 deg, we find that NeTT and mNeRF can achieve similar results, both with overall success rates more than 93%. However, the computational cost of NeTT is significantly lower than mNeRF in both training and pose estimation. Furthermore, we show that a NeTT trained for a single subject can generalize to synthesize high-fidelity DRRs and ensure robust pose estimations for all other subjects. Therefore, we suggest that NeTT is an attractive option for robust pose estimation using fluoroscopic projections

Image zooming based on sampling theorems

In this paper we introduce two digital zoom methods based on sampling theory and we study their mathematical foundation. The first one (usually known by the names of "sinc interpolation", "zero-padding" and "Fourier zoom") is commonly used by the image processing community