DGtal  1.5.beta
exampleHeatLaplace.cpp
1
17
24
25 #include <DGtal/helpers/StdDefs.h>
26
27 #include <DGtal/topology/DigitalSurface.h>
28 #include <DGtal/topology/DigitalSetBoundary.h>
29 #include <DGtal/topology/SetOfSurfels.h>
30 #include <DGtal/topology/LightImplicitDigitalSurface.h>
31
32 #include <DGtal/math/linalg/EigenSupport.h>
33
34 #include <DGtal/dec/DiscreteExteriorCalculus.h>
35 #include <DGtal/dec/DiscreteExteriorCalculusFactory.h>
36 #include <DGtal/dec/DiscreteExteriorCalculusSolver.h>
37 #include <DGtal/dec/VectorField.h>
38
40 #include <DGtal/geometry/surfaces/estimation/IIGeometricFunctors.h>
41 #include <DGtal/geometry/surfaces/estimation/IntegralInvariantCovarianceEstimator.h>
42
44 #include <DGtal/io/colormaps/ColorBrightnessColorMap.h>
45 #include <DGtal/io/colormaps/TickedColorMap.h>
47
48 #include <DGtal/images/IntervalForegroundPredicate.h>
49 #include <DGtal/images/imagesSetsUtils/SetFromImage.h>
50
51 #include <DGtal/shapes/parametric/Ball3D.h>
52 #include <DGtal/shapes/Shapes.h>
53 #include <DGtal/shapes/GaussDigitizer.h>
54
55 struct Options
56 {
57  double h;
60 };
61
63
64 using namespace DGtal;
65 using namespace Eigen;
66
68
69 typedef Z3i::Space Space;
72 typedef Z3i::Point Point;
73
75
77 {
78  return RealPoint( a.norm(), atan2( a[1], a[0] ), acos( a[2] ) );
79 }
80
82 std::function<double(const RealPoint&)> xx_function =
83  [] ( const RealPoint& p )
84 {
85  const RealPoint p_sphere = p / p.norm();
86  return p_sphere[0] * p_sphere[0];
87 };
88
89 std::function<double(const RealPoint&)> xx_derivative =
90  [] ( const RealPoint& p )
91 {
92  const RealPoint p_s = cartesian_to_spherical( p );
93  return 2. * cos( p_s[1] ) * cos( p_s[1] ) * ( 2 * cos( p_s[2] ) * cos( p_s[2] ) - sin( p_s[2] ) * sin( p_s[2] ) )
94  + 2. * ( sin( p_s[1] ) * sin( p_s[1] ) - cos( p_s[1] ) * cos( p_s[1] ) );
95 };
97
98 template <typename Shape>
99 void convergence(const Options& options, Shape& shape,
100  const std::function< double(const RealPoint&) >& input_function,
101  const std::function< double(const RealPoint&) >& result_function)
102 {
103  trace.beginBlock("Laplacian 3D");
104
105  trace.beginBlock("Extracting Digital Surface");
106
107  typedef Z3i::KSpace KSpace;
108
110  typedef GaussDigitizer<Z3i::Space, Shape> Digitizer;
111
112  Digitizer digitizer;
113  digitizer.attach(shape);
114  digitizer.init(shape.getLowerBound() + Z3i::Vector(-1,-1,-1), shape.getUpperBound() + Z3i::Vector(1,1,1), options.h);
115
116  Z3i::Domain domain = digitizer.getDomain();
117
118  Z3i::KSpace kspace;
119  bool ok = kspace.init(domain.lowerBound(), domain.upperBound(), true);
120  if( !ok ) std::cerr << "KSpace init failed" << std::endl;
121
123  typedef SetOfSurfels< KSpace, SurfelSet > MySetOfSurfels;
126
128  MySetOfSurfels theSetOfSurfels( kspace, surfAdj );
129  Surfaces<KSpace>::sMakeBoundary( theSetOfSurfels.surfelSet(),
130  kspace, digitizer,
131  domain.lowerBound(),
132  domain.upperBound() );
133  MyDigitalSurface digSurf( theSetOfSurfels );
135  trace.info() << "Digital Surface has " << digSurf.size() << " surfels." << std::endl;
136
137  trace.endBlock();
138
139  trace.beginBlock("Initializing Normal Functor");
142  CanonicSCellEmbedder canonicSCellEmbedder(kspace);
143
144  typedef functors::IINormalDirectionFunctor<Space> MyIINormalFunctor;
146
148
149  MyIINormalFunctor normalFunctor;
151
152  MyIINormalEstimator normalEstimator(normalFunctor);
153  normalEstimator.attach(kspace, digitizer);
155
156  normalEstimator.init(options.h, digSurf.begin(), digSurf.end());
158  trace.endBlock();
159
160  trace.beginBlock("Initializing DEC");
164
165  const Calculus calculus = CalculusFactory::createFromNSCells<2>(digSurf.begin(), digSurf.end(), normalEstimator, options.h);
167  trace.info() << calculus << std::endl;
168
169  trace.endBlock();
170  trace.beginBlock("Computing the input function");
172  Calculus::DualForm0 input_func(calculus);
173
174  for(auto itb = digSurf.begin(), ite = digSurf.end(); itb != ite; itb++)
175  {
176  const Calculus::Index i_calc = calculus.getCellIndex( kspace.unsigns( *itb ) );
177  input_func.myContainer( i_calc ) = input_function( options.h * canonicSCellEmbedder( *itb ) );
178  }
180  trace.endBlock();
181
182  trace.beginBlock("Computing the Laplace operator");
184  const double t = options.convolution_radius * pow(options.h, 2. / 3.);
185  const double K = log( - log1p( t ) ) + 2.;
186  const Calculus::DualIdentity0 laplace = calculus.heatLaplace<DUAL>(options.h, t, K);
188  trace.info() << "Matrix has " << ((double)laplace.myContainer.nonZeros() / (double)laplace.myContainer.size() * 100.) << "% of non-zeros elements." << std::endl;
189  trace.endBlock();
190
192  const Eigen::VectorXd laplace_result = (laplace * input_func).myContainer;
194  Eigen::VectorXd error( digSurf.size() );
195  Eigen::VectorXd real_laplacian_values( digSurf.size() );
196  Eigen::VectorXd estimated_laplacian_values( digSurf.size() );
197
198  int i = 0;
199  for(auto itb = digSurf.begin(), ite = digSurf.end(); itb != ite; itb++)
200  {
201  const Calculus::Index i_calc = calculus.getCellIndex( kspace.unsigns( *itb ) );
202
203  const RealPoint p = options.h * canonicSCellEmbedder( *itb );
204  const RealPoint p_normalized = p / p.norm();
205  const RealPoint p_s = cartesian_to_spherical( p );
206
207  const double real_laplacian_value = result_function( p_normalized );
208  const double estimated_laplacian_value = laplace_result( i_calc );
209
210  estimated_laplacian_values(i) = estimated_laplacian_value;
211  real_laplacian_values(i) = real_laplacian_value;
212
213  error(i) = estimated_laplacian_value - real_laplacian_value;
214
215  ++i;
216  }
217
218  trace.info() << "Estimated Laplacian Range : " << estimated_laplacian_values.minCoeff() << " / " << estimated_laplacian_values.maxCoeff() << std::endl;
219  trace.info() << "Real Laplacian Range : " << real_laplacian_values.minCoeff() << " / " << real_laplacian_values.maxCoeff() << std::endl;
220
221  trace.info() << "h = " << options.h << " t = " << t << " K = " << K << std::endl;
222  trace.info() << "Mean error = " << error.array().abs().mean() << " max error = " << error.array().abs().maxCoeff() << std::endl;
223
224  trace.endBlock();
225 }
226
227 int main()
228 {
229  Options options;
230
231  options.h = 0.1;
234
235  typedef Ball3D<Z3i::Space> Ball;
236  Ball ball(Point(0.0,0.0,0.0), 1.0);
237
238  std::function<double(const RealPoint&, const RealPoint&)> l2_distance =
239  [](const RealPoint& a, const RealPoint& b) { return (a - b).norm(); };
240
241  convergence<Ball>(options, ball, xx_function, xx_derivative);
242
243  return 0;
244 }
RealPoint getLowerBound() const
Definition: Astroid2D.h:122
RealPoint getUpperBound() const
Definition: Astroid2D.h:131
Aim: Model of the concept StarShaped3D represents any Sphere in the space.
Definition: Ball3D.h:61
Aim: Represents a set of n-1-cells in a nD space, together with adjacency relation between these cell...
Aim: This class provides static members to create DEC structures from various other DGtal structures.
Aim: DiscreteExteriorCalculus represents a calculus in the dec package. This is the main structure in...
Aim: A class for computing the Gauss digitization of some Euclidean shape, i.e. its intersection with...
void attach(ConstAlias< EuclideanShape > shape)
const Point & lowerBound() const
const Point & upperBound() const
Aim: This class implement an Integral Invariant estimator which computes for each surfel the covarian...
Aim: This class is a model of CCellularGridSpaceND. It represents the cubical grid as a cell complex,...
std::set< SCell > SurfelSet
Preferred type for defining a set of surfels (always signed cells).
bool init(const Point &lower, const Point &upper, bool isClosed)
Specifies the upper and lower bounds for the maximal cells in this space.
Cell unsigns(const SCell &p) const
Creates an unsigned cell from a signed one.
Aim: Implements basic operations that will be used in Point and Vector classes.
Definition: PointVector.h:593
double norm(const NormType type=L_2) const
Aim: A model of CDigitalSurfaceContainer which defines the digital surface as connected surfels....
Definition: SetOfSurfels.h:74
static void sMakeBoundary(SCellSet &aBoundary, const KSpace &aKSpace, const PointPredicate &pp, const Point &aLowerBound, const Point &aUpperBound)
void beginBlock(const std::string &keyword="")
std::ostream & info()
double endBlock()
Aim: A functor Matrix -> RealVector that returns the normal direction by diagonalizing the given cova...
PolyCalculus * calculus
Space::RealVector RealVector
SMesh::Index Index
DigitalSurface< MyDigitalSurfaceContainer > MyDigitalSurface
MyDigitalSurface::SurfelSet SurfelSet
DGtal is the top-level namespace which contains all DGtal functions and types.
Trace trace
Definition: Common.h:153
@ DUAL
Definition: Duality.h:62
MessageStream error
RealPoint cartesian_to_spherical(const RealPoint3D &a)
int main(int argc, char **argv)
MyPointD Point
Definition: testClone2.cpp:383
KSpace K
Domain domain
PointVector< 3, double > RealPoint