32 results about "Stochastic partial differential equation" patented technology

A fast and robust segmentation model for piecewise smooth images is provided. Local statistics in an energy formulation are provided as a functional. The shape gradient of this new functional gives a contour evolution controlled by local averaging of image intensities inside and outside the contour. Fast computation is realized by expressing terms as the result of convolutions implemented via recursive filters. Results are similar to the general Mumford-Shah model but realized faster without having to solve a Poisson partial differential equation at each iteration. Examples are provided. A system to implement segmentation methods is also provided.

The invention discloses a method for calculating a nonlinear partial differential equation by dual-grid iteration. The method comprises the following steps: (a) establishing a three-dimensional geometric model of the nonlinear partial differential equation; (b) performing grid dissection on the three-dimensional geometric model, and dividing into two sets of grids, namely grids A and girds B, wherein the grids A are non-fitted grids, and the grids B are polyhedral fitting grids; (c) interpolating initial and boundary data into non-fitting parts of the grids A by using interpolations with four orders or above; (d) decomposing the nonlinear partial differential equation into a plurality of linear equations by using an iterative technique, wherein the linear equation is solved by using the grids A and using a four-order algorithm, and interpolating into the grids B to obtain fields in the fitting grids B; (e) performing iterative computation in the grids B; (f) repeating the steps (d) and (e) until the solving is ended. Compared with the prior art, the method disclosed by the invention has the advantages of high calculation efficiency, low cost and high precision by adopting dual-grid solving.

The invention discloses a partial differential equation-based nano-particle size measurement method. The method includes the following steps that: 1) a nano-particle image I is inputted, pixel-level multiplication is performed on the filtering result of a mean curvature flow model and a PM model, so that a filtered image u can be obtained; 2) a region scalable fitting (RSF) model is adopted to segment the image u; 3) pixel calibration is carried out, the actual size of each pixel in the image can be obtained; 4) inadherent particles are selected out by means of the convexity (Cconv) of a target; and 5) least-square circle fitting is performed on the boundaries of the particles, so that the diameters of spherical nano-particles can be obtained, and the diameter rc of the internally tangent circle of the nano-particles, the diameter ri of the externally tangent circle of the nano-particles, and the sphericity of the nano-particles are obtained, wherein the sphericity of the nano-particles can be represented by an expression S=ri / rc. The method of the invention can be widely applied to the high-tech fields such as catalytic science, medical drugs, new materials, electric power industry and compound materials which require nano-particle size measurement technology.

A method of computing a continuous interpolation of a discrete set of three-dimensional (3D) balls, including generating an initial skin, wherein the initial skin is a surface comprised of splines and wherein the splines touch each ball along a circle that is tangent to the ball, solving a first differential equation to minimize the initial skin's surface area or solving a second differential equation to minimize a squared mean curvature of the initial skin's surface, wherein the result of solving the first or second differential equations is an updated skin; and repeating the steps of solving the first or second differential equations for the updated skin, and then, repeating the steps of solving the first or second differential equations for each subsequently updated skin until a desired skin is realized.

The invention discloses a denoising method of a strong noise pollution image on the basis of partial differential equation, mainly solving the problem of poor traditional denoising effect of the strong noise pollution image. The realization process comprises: (1) pretreating an input noise image u0, and recording the result as u; (2) calculating the partial derivative sum of the image u; (3) calculating the gradient module value of the image u; (4) according to the gradient and the gradient module value, building the partial differential equation; (5) calculating diffusion coefficients and psi in the partial differential equation; (6) utilizing the coefficients and psi, solving the partial differential equation to obtain a filter image; (7) calculating the peak signal to noise ratio PSNR of the filter image; and (8) repeating steps 2 to 7, when the PSNR value of the filter image output iteratively one time is smaller than that output iteratively in the previous time, stopping iteration, and outputting the previously iterated filter image. The invention has simple calculation and high operation speed, can better keep image texture details while smoothening strong noise and can be used for denoising a natural image with strong noise pollution.

The invention discloses a four-order partial differential equation image denoising method based on mathematical morphology. The method comprises the following steps: S1) adopting a mathematical morphology method for detecting a noise image edge; S2) calculating a gradient magnitude of the noise image; S3) establishing a partial differential equation according to the gradient operator of the mathematical morphology in S1) and the gradient magnitude in S2); S4) adopting an iteration method for solving the differential equation and acquiring a denoised image. According to the invention, image denoising is performed through the four-order partial differential equation based on mathematical morphology, the processed image edge is better kept and the visual effect is better.

The invention provides a method for designing a flexible mechanical arm disturbance observer based on a partial differential equation. The method includes the four steps that firstly, dynamic modeling of a flexible mechanical arm is conducted; secondly, the disturbance observer is designed; thirdly, stability of the disturbance observer is verified; fourthly, design is finished. According to the method, firstly the Hamilton principle is used, so that a PDE model of a whole system is obtained; then, based on the model, the reasonable disturbance observer is designed so that external unknown disturbance can be estimated; finally, a proper Lyapunov function is designed, so that the designed observer is analyzed and the stability of the observer is verified.