Analysis of high dimensional data is a common task. Often, small multiples are used to visualize 1 or 2 dimensions at a time, such as in a scatterplot matrix. Associating data points between different views can be difficult though, as the points are not fixed. Other times, dimensional reduction techniques are employed to summarize the whole dataset in one image, but individual dimensions are lost in this view. In this paper, we present a means of augmenting a dimensional reduction plot with isocontours to reintroduce the original dimensions. By applying this to each dimension in the original data, we create multiple views where the points are consistent, which facilitates their comparison. Our approach employs a combination of a novel, graph-based projection technique with a GPU accelerated implementation of moving least squares to interpolate space between the points. We also present evaluations of this approach both with a case study and with a user study.
There are many methods for interpolating between unstructured data points, including Barycentric linear interpolation, Sibson interpolation @cite_47 , and Moving Least Squares (MLS) @cite_9 . Of these, MLS offers the smoothest continuity. While MLS is often used in 3D applications such as surface reconstruction @cite_46 , it has also been applied to 2D applications such as image deformation, as in the work of @cite_23 where MLS is used to distort a grid of points according to a skeleton of control points. MLS has also be used to interpolate internal coordinates for higher order polygons @cite_14 . Our approach uses the deformation calculations from @cite_23 , but uses them to interpolate texture coordinates as in @cite_14 . Also, we use GPU acceleration to parallely perform the MLS calculation per pixel.
@cite_47 @cite_14 @cite_9 @cite_23 @cite_46
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Abstract Mobile laser scanning (MLS) has become a popular technique for road inventory, building modelling, infrastructure management, mobility assessment, etc. Meanwhile, due to the high mobility of MLS systems, it is easy to revisit interested areas. However, change detection using MLS data of street environment has seldom been studied. In this paper, an approach that combines occupancy grids and a distance-based method for change detection from MLS point clouds is proposed. Unlike conventional occupancy grids, our occupancy-based method models space based on scanning rays and local point distributions in 3D without voxelization. A local cylindrical reference frame is presented for the interpolation of occupancy between rays according to the scanning geometry. The Dempster–Shafer theory (DST) is utilized for both intra-data evidence fusion and inter-data consistency assessment. Occupancy of reference point cloud is fused at the location of target points and then the consistency is evaluated directly on the points. A point-to-triangle (PTT) distance-based method is combined to improve the occupancy-based method. Because it is robust to penetrable objects, e.g. vegetation, which cause self-conflicts when modelling occupancy. The combined method tackles irregular point density and occlusion problems, also eliminates false detections on penetrable objects. Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds. Many modern 3D reconstruction methods accumulate information volumetrically using truncated signed distance functions. While this usually imposes a regular grid with fixed voxel size, not all parts of a scene necessarily need to be represented at the same level of detail. For example, a flat table needs less detail than a highly structured keyboard on it. We introduce a novel representation for the volumetric 3D data that uses hash functions rather than trees for accessing individual blocks of the scene, but which still provides different resolution levels. We show that our data structure provides efficient access and manipulation functions that can be very well parallelised, and also describe an automatic way of choosing appropriate resolutions for different parts of the scene. We embed the novel representation in a system for simultaneous localization and mapping from RGB-D imagery and also investigate the implications of the irregular grid on interpolation routines. Finally, we evaluate our system in experiments, demonstrating state-of-the-art representation accuracy at typical frame-rates around 100 Hz, along with 40 memory savings. Various 3D reconstruction methods have enabled civil engineers to detect damage on a road surface. To achieve the millimeter accuracy required for road condition assessment, a disparity map with subpixel resolution needs to be used. However, none of the existing stereo matching algorithms are specially suitable for the reconstruction of the road surface. Hence in this paper, we propose a novel dense subpixel disparity estimation algorithm with high computational efficiency and robustness. This is achieved by first transforming the perspective view of the target frame into the reference view, which not only increases the accuracy of the block matching for the road surface but also improves the processing speed. The disparities are then estimated iteratively using our previously published algorithm, where the search range is propagated from three estimated neighboring disparities. Since the search range is obtained from the previous iteration, errors may occur when the propagated search range is not sufficient. Therefore, a correlation maxima verification is performed to rectify this issue, and the subpixel resolution is achieved by conducting a parabola interpolation enhancement. Furthermore, a novel disparity global refinement approach developed from the Markov random fields and fast bilateral stereo is introduced to further improve the accuracy of the estimated disparity map, where disparities are updated iteratively by minimizing the energy function that is related to their interpolated correlation polynomials. The algorithm is implemented in C language with a near real-time performance. The experimental results illustrate that the absolute error of the reconstruction varies from 0.1 to 3 mm.