Low-discrepancy point sampling of 2D manifolds for visual computing

Point distributions are used to sample surfaces for a wide variety of applications within the fields of graphics and computational geometry, such as point-based graphics, remeshing and area/volume measurement. The quality of such point distributions is important, and quality criteria are often application dependent. Common quality criteria include visual appearance, an even distribution whilst avoiding aliasing and other artifacts, and minimisation of the number of points required to accurately sample a surface. Previous work suggests that discrepancy measures the uniformity of a point distribution and hence a point distribution of minimal discrepancy is expected to be of high quality. We investigate discrepancy as a measure of sampling quality, and present a novel approach for generating low-discrepancy point distributions on parameterised surfaces. Our approach uses the idea of converting the 2D sampling problem into a ID problem by adaptively mapping a space-filling curve onto the surface. A ID sequence is then generated and used to sample the surface along the curve. The sampling process takes into account the parametric mapping, employing a corrective approach similar to histogram equalisation, to ensure that it gives a 2D low-discrepancy point distribution on the surface. The local sampling density can be controlled by a user-defined density function, e.g. to preserve local features, or to achieve desired data reduction rates. Experiments show that our approach efficiently generates low-discrepancy distributions on arbitrary parametric surfaces, demonstrating nearly as good results as popular low-discrepancy sampling methods designed for particular surfaces like planes and spheres. We develop a generalised notion of the standard discrepancy measure, which considers a broader set of sample shapes used to compute the discrepancy. In this more thorough testing, our sampling approach produces results superior to popular distributions. We also demonstrate that the point distributions produced by our approach closely adhere to the blue noise criterion, compared to the popular low-discrepancy methods tested, which show high levels of structure, undesirable for visual representation. Furthermore, we present novel sampling algorithms to generate low-discrepancy distributions on triangle meshes. To sample the mesh, it is cut into a disc topology, and a parameterisation is generated. Our sampling algorithm can then be used to sample the parameterised mesh, using robust methods for computing discrete differential properties of the surface. After these pre-processing steps, the sampling density can be adjusted in real-time. Experiments also show that our sampling approach can accurately resample existing meshes with low discrepancy, demonstrating error rates when reducing the mesh complexity as good as the best results in the literature. We present three applications of our mesh sampling algorithm. We first describe a point- based graphics sampling approach, which includes a global hole-filling algorithm. We investigate the coverage of sample discs for this approach, demonstrating results superior to random sampling and a popular low-discrepancy method. Moreover, we develop levels of detail and view dependent rendering approaches, providing very fine-grained density control with distance and angle, and silhouette enhancement. We further discuss a triangle- based remeshing technique, producing high quality, topologically unaltered meshes. Finally, we describe a complete framework for sampling and painting engineering prototype models. This approach provides density control according to surface texture, and gives full dithering control of the point sample distribution. Results exhibit high quality point distributions for painting that are invariant to surface orientation or complexity. The main contributions of this thesis are novel algorithms to generate high-quality density- controlled point distributions on parametric surfaces and triangular meshes. Qualitative assessment and discrepancy measures and blue noise criteria show their high sampling quality in general. We introduce generalised discrepancy measures which indicate that the sampling quality of our approach is superior to other low-discrepancy sampling techniques. Moreover, we present novel approaches towards remeshing, point-based rendering and robotic painting of prototypes by adapting our sampling algorithms and demonstrate the overall good quality of the results for these specific applications.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Low-discrepancy point sampling of 2D manifolds for visual computing

Point distributions are used to sample surfaces for a wide variety of applications within the fields of graphics and computational geometry, such as point-based graphics, remeshing and area/volume measurement. The quality of such point distributions is important, and quality criteria are often application dependent. Common quality criteria include visual appearance, an even distribution whilst avoiding aliasing and other artifacts, and minimisation of the number of points required to accurately sample a surface. Previous work suggests that discrepancy measures the uniformity of a point distribution and hence a point distribution of minimal discrepancy is expected to be of high quality. We investigate discrepancy as a measure of sampling quality, and present a novel approach for generating low-discrepancy point distributions on parameterised surfaces. Our approach uses the idea of converting the 2D sampling problem into a ID problem by adaptively mapping a space-filling curve onto the surface. A ID sequence is then generated and used to sample the surface along the curve. The sampling process takes into account the parametric mapping, employing a corrective approach similar to histogram equalisation, to ensure that it gives a 2D low-discrepancy point distribution on the surface. The local sampling density can be controlled by a user-defined density function, e.g. to preserve local features, or to achieve desired data reduction rates. Experiments show that our approach efficiently generates low-discrepancy distributions on arbitrary parametric surfaces, demonstrating nearly as good results as popular low-discrepancy sampling methods designed for particular surfaces like planes and spheres. We develop a generalised notion of the standard discrepancy measure, which considers a broader set of sample shapes used to compute the discrepancy. In this more thorough testing, our sampling approach produces results superior to popular distributions. We also demonstrate that the point distributions produced by our approach closely adhere to the blue noise criterion, compared to the popular low-discrepancy methods tested, which show high levels of structure, undesirable for visual representation. Furthermore, we present novel sampling algorithms to generate low-discrepancy distributions on triangle meshes. To sample the mesh, it is cut into a disc topology, and a parameterisation is generated. Our sampling algorithm can then be used to sample the parameterised mesh, using robust methods for computing discrete differential properties of the surface. After these pre-processing steps, the sampling density can be adjusted in real-time. Experiments also show that our sampling approach can accurately resample existing meshes with low discrepancy, demonstrating error rates when reducing the mesh complexity as good as the best results in the literature. We present three applications of our mesh sampling algorithm. We first describe a point- based graphics sampling approach, which includes a global hole-filling algorithm. We investigate the coverage of sample discs for this approach, demonstrating results superior to random sampling and a popular low-discrepancy method. Moreover, we develop levels of detail and view dependent rendering approaches, providing very fine-grained density control with distance and angle, and silhouette enhancement. We further discuss a triangle- based remeshing technique, producing high quality, topologically unaltered meshes. Finally, we describe a complete framework for sampling and painting engineering prototype models. This approach provides density control according to surface texture, and gives full dithering control of the point sample distribution. Results exhibit high quality point distributions for painting that are invariant to surface orientation or complexity. The main contributions of this thesis are novel algorithms to generate high-quality density- controlled point distributions on parametric surfaces and triangular meshes. Qualitative assessment and discrepancy measures and blue noise criteria show their high sampling quality in general. We introduce generalised discrepancy measures which indicate that the sampling quality of our approach is superior to other low-discrepancy sampling techniques. Moreover, we present novel approaches towards remeshing, point-based rendering and robotic painting of prototypes by adapting our sampling algorithms and demonstrate the overall good quality of the results for these specific applications.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Low-discrepancy point sampling of 2D manifolds for visual computing

Point distributions are used to sample surfaces for a wide variety of applications within the fields of graphics and computational geometry, such as point-based graphics, remeshing and area/volume measurement. The quality of such point distributions is important, and quality criteria are often application dependent. Common quality criteria include visual appearance, an even distribution whilst avoiding aliasing and other artifacts, and minimisation of the number of points required to accurately sample a surface. Previous work suggests that discrepancy measures the uniformity of a point distribution and hence a point distribution of minimal discrepancy is expected to be of high quality. We investigate discrepancy as a measure of sampling quality, and present a novel approach for generating low-discrepancy point distributions on parameterised surfaces. Our approach uses the idea of converting the 2D sampling problem into a ID problem by adaptively mapping a space-filling curve onto the surface. A ID sequence is then generated and used to sample the surface along the curve. The sampling process takes into account the parametric mapping, employing a corrective approach similar to histogram equalisation, to ensure that it gives a 2D low-discrepancy point distribution on the surface. The local sampling density can be controlled by a user-defined density function, e.g. to preserve local features, or to achieve desired data reduction rates. Experiments show that our approach efficiently generates low-discrepancy distributions on arbitrary parametric surfaces, demonstrating nearly as good results as popular low-discrepancy sampling methods designed for particular surfaces like planes and spheres. We develop a generalised notion of the standard discrepancy measure, which considers a broader set of sample shapes used to compute the discrepancy. In this more thorough testing, our sampling approach produces results superior to popular distributions. We also demonstrate that the point distributions produced by our approach closely adhere to the blue noise criterion, compared to the popular low-discrepancy methods tested, which show high levels of structure, undesirable for visual representation. Furthermore, we present novel sampling algorithms to generate low-discrepancy distributions on triangle meshes. To sample the mesh, it is cut into a disc topology, and a parameterisation is generated. Our sampling algorithm can then be used to sample the parameterised mesh, using robust methods for computing discrete differential properties of the surface. After these pre-processing steps, the sampling density can be adjusted in real-time. Experiments also show that our sampling approach can accurately resample existing meshes with low discrepancy, demonstrating error rates when reducing the mesh complexity as good as the best results in the literature. We present three applications of our mesh sampling algorithm. We first describe a point- based graphics sampling approach, which includes a global hole-filling algorithm. We investigate the coverage of sample discs for this approach, demonstrating results superior to random sampling and a popular low-discrepancy method. Moreover, we develop levels of detail and view dependent rendering approaches, providing very fine-grained density control with distance and angle, and silhouette enhancement. We further discuss a triangle- based remeshing technique, producing high quality, topologically unaltered meshes. Finally, we describe a complete framework for sampling and painting engineering prototype models. This approach provides density control according to surface texture, and gives full dithering control of the point sample distribution. Results exhibit high quality point distributions for painting that are invariant to surface orientation or complexity. The main contributions of this thesis are novel algorithms to generate high-quality density- controlled point distributions on parametric surfaces and triangular meshes. Qualitative assessment and discrepancy measures and blue noise criteria show their high sampling quality in general. We introduce generalised discrepancy measures which indicate that the sampling quality of our approach is superior to other low-discrepancy sampling techniques. Moreover, we present novel approaches towards remeshing, point-based rendering and robotic painting of prototypes by adapting our sampling algorithms and demonstrate the overall good quality of the results for these specific applications

Optimisation of surface coverage paths used by a non-contact robot painting system

This thesis proposes an efficient path planning technique for a non-contact optical “painting” system that produces surface images by moving a robot mounted laser across objects covered in photographic emulsion. In comparison to traditional 3D planning approaches (e.g. laminar slicing) the proposed algorithm dramatically reduces the overall path length by optimizing (i.e. minimizing) the amounts of movement between robot configurations required to position and orientate the laser. To do this the pixels of the image (i.e. points on the surface of the object) are sequenced using configuration space rather than Cartesian space. This technique extracts data from a CAD model and then calculates the configuration that the five degrees of freedom system needs to assume to expose individual pixels on the surface. The system then uses a closest point analysis on all the major joints to sequence the points and create an efficient path plan for the component. The implementation and testing of the algorithm demonstrates that sequencing points using a configuration based method tends to produce significantly shorter paths than other approaches to the sequencing problem. The path planner was tested with components ranging from simple to complex and the paths generated demonstrated both the versatility and feasibility of the approach

A framework for hull form reverse engineering and geometry integration into numerical simulations

The thesis presents a ship hull form specific reverse engineering and CAD integration framework. The reverse engineering part proposes three alternative suitable reconstruction approaches namely curves network, direct surface fitting, and triangulated surface reconstruction. The CAD integration part includes surface healing, region identification, and domain preparation strategies which used to adapt the CAD model to downstream application requirements. In general, the developed framework bridges a point cloud and a CAD model obtained from IGES and STL file into downstream applications

Mini-Workshop: Analytical and Numerical Methods in Image and Surface Processing

The workshop successfully brought together researchers from mathematical analysis, numerical mathematics, computer graphics and image processing. The focus was on variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, image and surface denoising based on geometric evolution problems in image and surface fairing, physical modeling of surfaces, the restoration of images and surfaces using higher order variational formulations

Texture Segregation By Visual Cortex: Perceptual Grouping, Attention, and Learning

A neural model is proposed of how laminar interactions in the visual cortex may learn and recognize object texture and form boundaries. The model brings together five interacting processes: region-based texture classification, contour-based boundary grouping, surface filling-in, spatial attention, and object attention. The model shows how form boundaries can determine regions in which surface filling-in occurs; how surface filling-in interacts with spatial attention to generate a form-fitting distribution of spatial attention, or attentional shroud; how the strongest shroud can inhibit weaker shrouds; and how the winning shroud regulates learning of texture categories, and thus the allocation of object attention. The model can discriminate abutted textures with blurred boundaries and is sensitive to texture boundary attributes like discontinuities in orientation and texture flow curvature as well as to relative orientations of texture elements. The model quantitatively fits a large set of human psychophysical data on orientation-based textures. Object boundar output of the model is compared to computer vision algorithms using a set of human segmented photographic images. The model classifies textures and suppresses noise using a multiple scale oriented filterbank and a distributed Adaptive Resonance Theory (dART) classifier. The matched signal between the bottom-up texture inputs and top-down learned texture categories is utilized by oriented competitive and cooperative grouping processes to generate texture boundaries that control surface filling-in and spatial attention. Topdown modulatory attentional feedback from boundary and surface representations to early filtering stages results in enhanced texture boundaries and more efficient learning of texture within attended surface regions. Surface-based attention also provides a self-supervising training signal for learning new textures. Importance of the surface-based attentional feedback in texture learning and classification is tested using a set of textured images from the Brodatz micro-texture album. Benchmark studies vary from 95.1% to 98.6% with attention, and from 90.6% to 93.2% without attention.Air Force Office of Scientific Research (F49620-01-1-0397, F49620-01-1-0423); National Science Foundation (SBE-0354378); Office of Naval Research (N00014-01-1-0624