- Generated by
1.8.14
|
Woolz Image Processing
Version 1.8.3
|
Functions for creating and manipulating basis functions. More...
Data Structures | |
| struct | _WlzBasisFnMapData3D |
| Used to memorise the nodes of a mesh element between 3D distance function evaluation calls. More... | |
Typedefs | |
| typedef struct _WlzBasisFnMapData3D | WlzBasisFnMapData3D |
Functions | |
| WlzErrorNum | WlzBasisFnFree (WlzBasisFn *basisFn) |
| Free's the given basis function. More... | |
| WlzDVertex2 | WlzBasisFnValuePoly2D (WlzBasisFn *basisFn, WlzDVertex2 srcVx) |
| Calculates the value for the given vertex using a 2D polynomial basis function. This is not a basis function just a polynomial, but it makes sense for it to be incuded in the basis functions since they have a polynomial component. More... | |
| WlzDVertex2 | WlzBasisFnValueGauss2D (WlzBasisFn *basisFn, WlzDVertex2 srcVx) |
| Calculates the value for the given vertex using a 2D Gaussian basis function. More... | |
| WlzDVertex2 | WlzBasisFnValueMQ2D (WlzBasisFn *basisFn, WlzDVertex2 srcVx) |
| Calculates the value for the given vertex using a 2D multiquadric basis function. More... | |
| WlzDVertex3 | WlzBasisFnValueMQ3D (WlzBasisFn *basisFn, WlzDVertex3 srcVx) |
| Calculates the displacement value for the given vertex using a 3D multiquadric basis function. More... | |
| WlzDVertex2 | WlzBasisFnValueIMQ2D (WlzBasisFn *basisFn, WlzDVertex2 srcVx) |
| Calculates the value for the given vertex using a 2D inverse multiquadric basis function. More... | |
| WlzDVertex3 | WlzBasisFnValueIMQ3D (WlzBasisFn *basisFn, WlzDVertex3 srcVx) |
| Calculates the displacement value for the given vertex using a 3D inverse multiquadric basis function. More... | |
| WlzDVertex2 | WlzBasisFnValueTPS2D (WlzBasisFn *basisFn, WlzDVertex2 srcVx) |
| Calculates the value for the given vertex using a 2D thin plate spline basis function. More... | |
| WlzDVertex2 | WlzBasisFnValueConf2D (WlzBasisFn *basisFn, WlzDVertex2 srcVx) |
| Calculates the value for the given vertex using a 2D conformal polynomial basis function. More... | |
| WlzDVertex3 | WlzBasisFnValueMOS3D (WlzBasisFn *basisFn, WlzDVertex3 srcVx) |
| Calculates the value for the given vertex using a 3D multiorder basis function: \[ \phi(r) = \frac{1}{4 \pi \delta^2 r} (1 - \frac{w}{w - v} e^{- \sqrt{v} r} + \frac{v}{w - v} e^{- \sqrt{w} r}) \] \[ v = \frac{1 + \sqrt{1 - 4 \pi \tau^2 \delta^2}}{2 \tau^2} \] \[ w = \frac{1 - \sqrt{1 - 4 \pi \tau^2 \delta^2}}{2 \tau^2} \] . More... | |
| double | WlzBasisFnValueScalarMOS3D (WlzBasisFn *basisFn, WlzDVertex3 srcVx) |
| Calculates the value for the given vertex using a scalar 3D multiorder basis function: \[ \phi(r) = \frac{1}{4 \pi \delta^2 r} (1 - \frac{w}{w - v} e^{- \sqrt{v} r} + \frac{v}{w - v} e^{- \sqrt{w} r}) \] \[ v = \frac{1 + \sqrt{1 - 4 \pi \tau^2 \delta^2}}{2 \tau^2} \] \[ w = \frac{1 - \sqrt{1 - 4 \pi \tau^2 \delta^2}}{2 \tau^2} \] . More... | |
| double | WlzBasisFnValueMOSPhi (double r, double delta, double tau) |
| Computes the value of a single multiorder radial basis function: \[ \phi(r) = \frac{1}{4 \pi \delta^2 r} (1 - \frac{w}{w - v} e^{- \sqrt{v} r} + \frac{v}{w - v} e^{- \sqrt{w} r}) \] \[ v = \frac{1 + \sqrt{1 - 4 \pi \tau^2 \delta^2}}{2 \tau^2} \] \[ w = \frac{1 - \sqrt{1 - 4 \pi \tau^2 \delta^2}}{2 \tau^2} \] . More... | |
| WlzBasisFn * | WlzBasisFnGauss2DFromCPts (int nPts, WlzDVertex2 *dPts, WlzDVertex2 *sPts, double delta, WlzBasisFn *prvBasisFn, WlzCMesh2D *mesh, WlzErrorNum *dstErr) |
| Creates a new Gaussian basis function. More... | |
| WlzBasisFn * | WlzBasisFnPoly2DFromCPts (int nPts, int order, WlzDVertex2 *dPts, WlzDVertex2 *sPts, WlzErrorNum *dstErr) |
| Creates a new polynomial basis function. More... | |
| WlzBasisFn * | WlzBasisFnConf2DFromCPts (int nPts, int order, WlzDVertex2 *dPts, WlzDVertex2 *sPts, WlzErrorNum *dstErr) |
| Creates a new conformal basis function. More... | |
| WlzBasisFn * | WlzBasisFnMQ2DFromCPts (int nPts, WlzDVertex2 *dPts, WlzDVertex2 *sPts, double delta, WlzBasisFn *prvBasisFn, WlzCMesh2D *mesh, WlzErrorNum *dstErr) |
| Creates a new multiquadric basis function. More... | |
| WlzBasisFn * | WlzBasisFnMQ3DFromCPts (int nPts, WlzDVertex3 *dPts, WlzDVertex3 *sPts, double delta, WlzBasisFn *prvBasisFn, WlzCMesh3D *mesh, WlzErrorNum *dstErr) |
| Creates a new multiquadric basis function. More... | |
| WlzBasisFn * | WlzBasisFnIMQ2DFromCPts (int nPts, WlzDVertex2 *dPts, WlzDVertex2 *sPts, double delta, WlzBasisFn *prvBasisFn, WlzCMesh2D *mesh, WlzErrorNum *dstErr) |
| Creates a new inverse-multiquadric basis function. More... | |
| WlzBasisFn * | WlzBasisFnIMQ3DFromCPts (int nPts, WlzDVertex3 *dPts, WlzDVertex3 *sPts, double delta, WlzBasisFn *prvBasisFn, WlzCMesh3D *mesh, WlzErrorNum *dstErr) |
| Creates a new inverse-multiquadric basis function. More... | |
| WlzBasisFn * | WlzBasisFnTPS2DFromCPts (int nPts, WlzDVertex2 *dPts, WlzDVertex2 *sPts, WlzBasisFn *prvBasisFn, WlzCMesh2D *mesh, WlzErrorNum *dstErr) |
| Creates a new thin plate spline basis function. More... | |
| WlzBasisFn * | WlzBasisFnMOS3DFromCPts (int nPts, WlzDVertex2 *dPts, WlzDVertex2 *sPts, double *alpha, double *param, WlzErrorNum *dstErr) |
| Creates a new 3D multi order spline basis function: \[ \phi(r) = \frac{1}{4 \pi \delta^2 r} (1 - \frac{w}{w - v} e^{- \sqrt{v} r} + \frac{v}{w - v} e^{- \sqrt{w} r}) \] \[ v = \frac{1 + \sqrt{1 - 4 \pi \tau^2 \delta^2}}{2 \tau^2} \] \[ w = \frac{1 - \sqrt{1 - 4 \pi \tau^2 \delta^2}}{2 \tau^2} \] \[ f(\mathbf{x}) = P(\mathbf{x}) + \sum_{i=1}^{n}{\lambda_i \phi(r_i)} \] \[ r_i = |\mathbf{x} - \mathbf{x'_i}| \] The multi order spline may either be an exact interpolating function or one which approximates the given control points. In the approximating case values for the regularization parameters should be given, with the regularization parameters \(\alpha_i\) given by: \[ H[f] = \beta[f] + \sum_{i=1}^{n}{\frac{(y_i - f(x))^2}{\alpha_i}} \] Giving the design equation: \[ \left( \begin{array}{cccccccc} 0 & 0 & 0 & 0 & 1 & 1 & \cdots & 1 \\ 0 & 0 & 0 & 0 & x_1 & x_2 & \cdots & x_n \\ 0 & 0 & 0 & 0 & y_1 & y_2 & \cdots & y_n \\ 0 & 0 & 0 & 0 & z_1 & z_2 & \cdots & z_n \\ 1 & x_1 & y_1 & z_1 & \phi(r_{11}) + \alpha_1 & \phi(r_{12}) & \cdots & \phi(r_{1n}) \\ \dotfill \\ 1 & x_n & y_n & z_n & \phi(r_{n1}) & \phi(r_{n2}) & \cdots & \phi(r_{nn} + \alpha_n) \end{array} \right) \left( \begin{array}{c} a_o \\ a_1 \\ a_2 \\ a_3 \\ \lambda_1 \\ \lambda_1 \\ \vdots \\ \lambda_n \end{array} \right) = \left( \begin{array}{c} 0 \\ 0 \\ 0 \\ 0 \\ f(\mathbf{x_1}) \\ f(\mathbf{x_1}) \\ \vdots \\ f(\mathbf{x_n}) \end{array} \right) \] The vertex values with components \(x\), \(y \) and \(z\) are used to solve for the four polynomial coefficients and the three basis function weights \(\lambda\), \(\mu\) and \(\nu\). The given values of \(\lambda\) and \(\tau\) are constrained by \(\lambda > 0, \tau > 0\) and \(\lambda \tau < 0.5\). More... | |
| WlzBasisFn * | WlzBasisFnScalarMOS3DFromCPts (int nPts, WlzDVertex3 *cPts, double *cVal, double *alpha, double *param, WlzErrorNum *dstErr) |
| Computes a new 3D multi order spline basis function which either interpolates or approximates the given scalar values. See WlzBasisFnMOS3DFromCPts() for details of the multi order spline. The given values of \(\lambda\) and \(\tau\) are constrained by \(\lambda > 0, \tau > 0\) and \(\lambda \tau < 0.5\). More... | |
Functions for creating and manipulating basis functions.
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
| typedef struct _WlzBasisFnMapData3D WlzBasisFnMapData3D |
1.8.14