Image segmentation and preserve the boundary of the image using b-spline basis

This paper focuses the knot insertion in the B-spline collocation matrix, with nonnegative determinants in all n x n sub-matrices. Further by relating the number of zeros in B-spline basis as well as changes (sign changes) in the sequence of its B-spline coefficients. From this relation, we obtained an accurate characterization when interpolation by B-splines correlates with the changes leads uniqueness and this ensures the optimal solution. Simultaneously we computed the knot insertion matrix and B-spline collocation matrix and its sub-matrices having nonnegative determinants. The totality of the knot insertion matrix and B-spline collocation matrix is demonstrated in the concluding section by using the input image and shows that these concepts are fit to apply and reduce the errors through mean square error and PSNR values

Creases and boundary conditions for subdivision curves

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

Creases and boundary conditions for subdivision curves

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

Creases and boundary conditions for subdivision curves

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

Creases and boundary conditions for subdivision curves

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

A Tidal Level Prediction Approach Based on BP Neural Network and Cubic B-Spline Curve with Knot Insertion Algorithm

Tide levels depend on both long-term astronomical effects that are mainly affected by moon and sun and short-term meteorological effects generated by severe weather conditions like storm surge. Storm surge caused by typhoons will impose serious security risks and threats on the coastal residents’ safety in production, property, and life. Due to the challenges of nonperiodic and incontinuous tidal level record data and the influence of multimeteorological factors, the existing methods cannot predict the tide levels affected by typhoons precisely. This paper targets to explore a more advanced method for forecasting the tide levels of storm surge caused by typhoons. First, on the basis of successive five-year tide level and typhoon data at Luchaogang, China, a BP neural network model is developed using six parameters of typhoons as input parameters and the relevant tide level data as output parameters. Then, for an improved forecasting accuracy, cubic B-spline curve with knot insertion algorithm is combined with the BP model to conduct smooth processing of the predicted points and thus the smoothed prediction curve of tidal level has been obtained. By using the data of the fifth year as the testing sample, the predicted results by the two methods are compared. The experimental results have shown that the latter approach has higher accuracy in forecasting tidal level of storm surge caused by typhoons, and the combined prediction approach provides a powerful tool for defending and reducing storm surge disaster.

Adjoint Optimisation of Internal Turbine Cooling Channel Using NURBS-Based Automatic and Adaptive Parametrisation Method

A well-formulated design space parametrisation is the key to the success of design optimisation. Most parametrisation methods require manual set-up which typically results in a restricted design space and impedes the generation of superior designs which may be found outside this restricted envelope. In this work, we adopt a NURBS-based automatic and adaptive parametrisation approach where the optimisation begins in a coarser design space and adapts to finer parametrisation during the optimisation. Our approach takes CAD descriptions as input and to alter the shape perturbs the control points of the NURBS patches that form the boundary representation. Driven by adjoint sensitivity information the control net is adaptively enriched using knot insertion. The sensitivity-driven parametrisation method is applied here to reduce the pressure loss of a U-bend passage of a turbine blade serpentine cooling channel.

Approximate Merging B-Spline Curves via Least Square Approximation

An algorithm of B-spline curve approximate merging of two adjacent B-spline curves is presented in this paper. In this algorithm, the approximation error between two curves is computed using norm which is known as best least square approximation. We develop a method based on weighed and constrained least squares approximation, which adds a weight function in object function to reduce error of merging. The knot insertion algorithm is also developed to meet the error tolerance.

Conformal and G1 Continuous Connection of NURBS Curves

This paper converts a NURBS curve to piecewise rational Bézier curves by knot insertion algorithm, and then discusses the algorithm of continuous connection of NURBS curves. Meanwhile, explores the method to keep the same shape of the NURBS curves after connecting through the point translation and vector rotation theory. Finally, gives an instance to verify the validity of the algorithm.