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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,99 @@ | ||
| """Take 2 clouds of points, source and target, and morph | ||
| source on target using thin plate splines as a model. | ||
| The fitting minimizes the distance to the target surface | ||
| using algorithms available in the scipy.optimize package.""" | ||
| from vtkplotter import * | ||
| import scipy.optimize as opt | ||
| import numpy as np | ||
| np.random.seed(0) | ||
|
|
||
| class Morpher: | ||
| def __init__(self): | ||
| self.source = None | ||
| self.morphed_source = None | ||
| self.target = None | ||
| self.bound = None | ||
| self.method = "SLSQP" # 'SLSQP', 'L-BFGS-B', 'TNC' ... | ||
| self.fitTolerance = 1e-6 | ||
| self.params = [] | ||
| self.fitResult = None | ||
| self.chi2 = 1.0e30 | ||
| self.ndf = None | ||
| self.ptsource = [] | ||
| self.pttarget = [] | ||
|
|
||
| def _func(self, pars): | ||
| self.params = np.array(pars) | ||
|
|
||
| ptmoved = np.multiply((self.pttarget-self.ptsource).T, (1+self.params)).T + self.ptsource | ||
| self.morphed_source = thinPlateSpline(self.source, self.ptsource, ptmoved) | ||
|
|
||
| d = self.morphed_source.getPoints() - self.target.getPoints() | ||
| chi2 = np.sum(np.multiply(d,d))/self.ndf | ||
| if chi2 < self.chi2: | ||
| print("Emin ->", chi2) | ||
| self.chi2 = chi2 | ||
| return chi2 | ||
|
|
||
| # ------------------------------------------------------- Fit | ||
| def morph(self): | ||
|
|
||
| print("\n..minimizing with " + self.method) | ||
| self.morphed_source = self.source.clone() | ||
|
|
||
| indexes = list(range(0,self.source.N(), int(self.source.N()/self.ndf))) | ||
| self.ptsource = self.source.getPoints()[indexes] | ||
| self.pttarget = self.target.getPoints()[indexes] | ||
| self.ndf = len(indexes) | ||
|
|
||
| bnds = [(-self.bound, self.bound)] * self.ndf | ||
| x0 = [0.0] * self.ndf # initial guess | ||
| res = opt.minimize(self._func, x0, | ||
| bounds=bnds, | ||
| method=self.method, | ||
| tol=self.fitTolerance) | ||
| # recalc for all pts: | ||
| self._func(res["x"]) | ||
| print("\nFinal fit score", res["fun"]) | ||
| self.fitResult = res | ||
|
|
||
| # ------------------------------------------------------- Visualization | ||
| def draw_shapes(self): | ||
| sb = self.source.bounds() | ||
| x1, x2, y1, y2, z1, z2 = sb | ||
| maxb = max(x2-x1, y2-y1) | ||
| grid0 = Grid(self.source.centerOfMass(), sx=maxb, sy=maxb, resx=40, resy=40) | ||
| T = self.morphed_source.getTransform() | ||
| grid1 = grid0.alpha(0.3).clone().transformMesh(T) # warp the grid | ||
|
|
||
| text1 = Text(__doc__, c="k") | ||
| text2 = Text("morphed vs target\nn.d.f.="+str(self.ndf), c="k") | ||
| arrows = Arrows(self.ptsource, self.pttarget, c='gray', alpha=0.5, s=1) | ||
|
|
||
| self.morphed_source.pointSize(10).c('g') | ||
| show(grid0, self.source, self.target, arrows, text1, at=0, N=2, bg="w", axes=0) | ||
| show(grid1, self.morphed_source, self.target, text2, at=1, zoom=1.2, interactive=1) | ||
|
|
||
|
|
||
| ################################# | ||
| if __name__ == "__main__": | ||
|
|
||
| mr = Morpher() | ||
|
|
||
| # make up a random cloud and distort it | ||
| pts_s = np.random.randn(100, 3) | ||
| pts_t = np.array(pts_s) +np.sin(2*pts_s)/5 | ||
| pts_s[:,2] = 0 # let's make it 2D | ||
| pts_t[:,2] = 0 | ||
|
|
||
| mr.source = Points(pts_s, r=10, c="g", alpha=1) | ||
| mr.target = Points(pts_t, r=10, c="r", alpha=1).rotateZ(10) # add rotation too | ||
|
|
||
| mr.bound = 1 # limits the parameter value | ||
| mr.ndf = 10 # fit degree (nr of degrees of freedom) | ||
|
|
||
| mr.morph() | ||
|
|
||
| #print("Result of parameter fit:\n", mr.params) | ||
| #now mr.msource contains the modified/morphed source. | ||
| mr.draw_shapes() |
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