30 results about "Elliptic partial differential equation" patented technology

A system and method for designing a progressive lens. Mean power is specified at points distributed over the entire surface of the lens and lens height is specified around the edge of the lens. Lens height is determined at the points consistent with the specified mean power and the lens edge height in part by solving a partial differential equation of the elliptic type subject to the lens edge height as a boundary condition. A successive over-relaxation technique may be employed to converge on the solution to the partial differential equation, and an over-relaxation factor may be determined to most efficiently relax the equation.

We describe a method of processing an EEG and / or MEG signal to generate image data representing a 3D current distribution, J, within the brain, the method comprising: capturing a plurality of electric and / or magnetic measurements from the exterior of the head; solving an integral equation for a part of said current distribution to generate said image data representing said 3D current distribution, wherein said integral equation comprises an integral of a first function representing said part of said current distribution and of a second function (∇τvs (r, τ)) representing the geometry and conductivity of the head independent of said current distribution; wherein said solving comprises: modelling the head as at least two regions separated by at least one internal boundary, and solving a set of partial differential equations, one for each said internal region, each partial differential equation comprising a geometry-conductivity function (w(r, τ)) representing the geometry and conductivity of the respective region, wherein said solving is subject to a boundary condition that either i) the gradients of the functions across the or each said internal boundary are smooth when conductivity is taken into account, or ii) a normal component of the electric field of said part of said current distribution is continuous across the or each said internal boundary, and wherein said geometry-conductivity function for an outermost said region of said head defines said second function (∇Tvs (r, τ))

A method for modeling a three dimensional shape of object using a level set solution on a partial differential equation derived from a Helmholtz reciprocity condition is provided. The method includes the steps of: a) inputting an image pair satisfying a Helmholtz reciprocity condition; b) performing an optical correction and simultaneously performing a geometric correction; c) performing a camera selection to select cameras capable of seeing a point (X, Y, Z), and defining and calculating a cost function by the Helmholtz reciprocity condition; d) calculating a speed function of a PDE that minimizes the cost function obtained in the step c); and e) generating a three dimension mesh model from a set of points configuring the object surface provided from the step d), and deciding a final three dimension mesh model by comparing cost function values.

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 present invention provides a method which is used for calculating Thevenin equivalent parameters of power system. The active power and reactive power of a tidal current equation are respectively used for differentiating the Thevenin equivalent parameters so as to form a total differential equation system; the total differential equation system is solved with the Thevenin equivalent parametersas variables, so as to acquire the Thevenin equivalent parameters. The method overcomes the serious error in the existing calculating which assumes the invariable Thevenin equivalent parameters between two time steps, has the characteristics of strong adaptability, simple use and small amount of calculation, and can be used for analysis, calculation and on-site installation of the power system which requires a Thevenin equivalent system.

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.

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.