A rational cubic spline with tension

A rational cubic spline curve is described which has tension control parameters for manipulating the shape of the curve. The spline is presented in both interpolatory and rational B-spline forms, and the behaviour of the resulting representations is analysed with respect to variation of the control parameters

Constrained Interpolation And Shape Preserving Approximation By Space Curves [QA297.6. K82 2006 f rb].

Dua jenis masalah rekabentuk lengkung telah ipertimbangkan. Terlebih dahulu kami mempertimbangkan interpolasi satu set titik data ruang yang bertertib dengan satu lengkung licin tertakluk kepada satu set satah kekangan yang berbentuk terhingga atau tak terhingga di mana garis cebis demi cebis yang menyambung titik data secara berturutan tidak bersilang dengan satah kekangan. Two types of curve designing problem have been considered. We first consider the interpolation of a given set of ordered spatial data points by a smooth curve in the presence of a set of finite or infinite constraint planes, where the polyline joining consecutive data points does not intersect with the constraint planes

Parametric Interpolation To Scattered Data [QA281. A995 2008 f rb].

Dua skema interpolasi berparameter yang mengandungi interpolasi global untuk data tersebar am dan interpolasi pengekalan-kepositifan setempat data tersebar positif dibincangkan. Two schemes of parametric interpolation consisting of a global scheme to interpolate general scattered data and a local positivity-preserving scheme to interpolate positive scattered data are described

Video Data Compression by Progressive Iterative Approximation

In the present paper, the B-spline curve is used for reducing the entropy of video data. We consider the color or luminance variations of a spatial position in a series of frames as input data points in Euclidean space R or R3. The progressive and iterative approximation (PIA) method is a direct and intuitive way of generating curve series of high and higher fitting accuracy. The video data points are approximated using progressive and iterative approximation for least square (LSPIA) fitting. The Lossless video data compression is done through storing the B-spline curve control points (CPs) and the difference between fitted and original video data. The proposed method is applied to two classes of synthetically produced and naturally recorded video sequences and makes a reduction in the entropy of both. However, this reduction is higher for syntactically created than those naturally produced. The comparative analysis of experiments on a variety of video sequences suggests that the entropy of output video data is much less than that of input video data

Vectorizing binary image boundaries with symmetric shape detection, bisection and optimal parameterization

Binary image boundary vectorization is the process of converting raster images into vector images represented with a sequence of Bézier curves. Two main factors in reconstructing parametric curves are to approximate the underlying structure of the boundaries as much as possible while using as few curves as possible. Existing methods do not perform well when considering both of these two main factors. In this article, we mimic the process of human vectorizing image boundaries by first segmenting the boundary points into multiple segments with the corner points. For the boundary points in each segment, we adopt the bisection method to find the largest number of points, which a single curve can fit. More curves will be added if the fitting error is larger than a predefined threshold. The process is repeated until all the points in the segment are fitted, thus minimizing the number of Bézier curves. Besides, symmetric image boundaries can be detected and used to further decrease the number of curves required. Our method can also choose the optimal parameterization method case by case to further reduce the fitting error. We make a comparison with both new and classical methods and show that our method outperforms them

08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

A kinematic-geometric model based on ankles’ depth trajectory in frontal plane for gait analysis using a single RGB-D camera

International audienceThe emergence of RGB-D cameras and the development of pose estimation algorithms offer opportunities in biomechanics. However, some challenges still remain when using them for gait analysis, including noise which leads to misidentification of gait events and inaccuracy.Therefore, we present a novel kinematic-geometric model for spatio-temporal gait analysis, based on ankles’ trajectory in the frontal plane and distance-to-camera data (depth). Our approach consists of three main steps: identification of the gait pattern and modeling via parameterized curves, development of a fitting algorithm, and computation of locomotive indices. The proposed fitting algorithm applies on both ankles’ depth data simultaneously, by minimizing through numerical optimization some geometric and biomechanical error functions. For validation, 15 subjects were asked to walk inside the walkway of the OptoGait, while the OptoGait and an RGB-D camera (Microsoft Azure Kinect) were both recording. Then, the spatiotemporal parameters of both feet were computed using the OptoGait and the proposed model. Validation results show that the proposed model yields good to excellent absolute statistical agreement (0.86≤Rc≤ 0.99). Our kinematic-geometric model offers several benefits: (1) It relies only on the ankles’ depth trajectory both for gait events extraction and spatio-temporal parameters’ calculation; (2) it is usablewith any kind of RGB-D camera or even with 3D marker-based motion analysis systems in absence of toes’ and heels’ markers; and (3) it enables improving the results by denoising and smoothing the ankles’ depth trajectory. Hence, the proposed kinematic-geometric model facilitates the development of portable markerless systems for accurate gait analysis