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    00001 /************************************************************************/
    00002 /*                                                                      */
    00003 /*               Copyright 2002-2004 by Ullrich Koethe                  */
    00004 /*       Cognitive Systems Group, University of Hamburg, Germany        */
    00005 /*                                                                      */
    00006 /*    This file is part of the VIGRA computer vision library.           */
    00007 /*    ( Version 1.5.0, Dec 07 2006 )                                    */
    00008 /*    The VIGRA Website is                                              */
    00009 /*        http://kogs-www.informatik.uni-hamburg.de/~koethe/vigra/      */
    00010 /*    Please direct questions, bug reports, and contributions to        */
    00011 /*        koethe@informatik.uni-hamburg.de          or                  */
    00012 /*        vigra@kogs1.informatik.uni-hamburg.de                         */
    00013 /*                                                                      */
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    00022 /*                                                                      */
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    00025 /*    Software.                                                         */
    00026 /*                                                                      */
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    00035 /*                                                                      */
    00036 /************************************************************************/
    00037
    00038 #ifndef VIGRA_ORIENTEDTENSORFILTERS_HXX
    00039 #define VIGRA_ORIENTEDTENSORFILTERS_HXX
    00040
    00041 #include <cmath>
    00042 #include "utilities.hxx"
    00043 #include "initimage.hxx"
    00044 #include "stdconvolution.hxx"
    00045
    00046 namespace vigra {
    00047
    00048 /** \addtogroup TensorImaging Tensor Image Processing
    00049 */
    00050 //@{
    00051
    00052 /********************************************************/
    00053 /*                                                      */
    00054 /*                     hourGlassFilter                  */
    00055 /*                                                      */
    00056 /********************************************************/
    00057
    00058 /** \brief Anisotropic tensor smoothing with the hourglass filter.
    00059
    00060     This function implements anisotropic tensor smoothing by an
    00061     hourglass-shaped filters as described in
    00062
    00063     U. K÷the: <a href="http://kogs-www.informatik.uni-hamburg.de/~koethe/papers/abstracts/structureTensor.html">
    00064     <i>"Edge and Junction Detection with an Improved Structure Tensor"</i></a>,
    00065      in: Proc. of 25th DAGM Symposium, Magdeburg 2003, Lecture Notes in Computer Science 2781,
    00066      pp. 25-32, Heidelberg: Springer, 2003
    00067
    00068     It is closely related to the structure tensor (see
    00069     \link CommonConvolutionFilters#structureTensor structureTensor\endlink()), but
    00070     replaces the linear tensor smoothing with a smoothing along edges only.
    00071     Smoothing accross edges is largely suppressed. This means that the
    00072     image structure is preserved much better because nearby features
    00073     such as parallel edges are not blended into each other.
    00074
    00075     The hourglass filter is typically applied to a gradient tensor, i.e. the
    00076     Euclidean product of the gradient with itself, which can be obtained by a
    00077     gradient operator followed with \ref vectorToTensor(), see example below.
    00078     The hourglass shape of the filter can be interpreted as indicating the likely
    00079     continuations of a local edge element. The parameter <tt>sigma</tt> determines
    00080     the radius of the hourglass (i.e. how far the influence of the edge element
    00081     reaches), and <tt>rho</tt> controls its opening angle (i.e. how narrow the
    00082     edge orientation os followed). Recommended values are <tt>sigma = 1.4</tt>
    00083     (or, more generally, two to three times the scale of the gradient operator
    00084     used in the first step), and <tt>rho = 0.4</tt> which corresponds to an
    00085     opening angle of 22.5 degrees to either side of the edge.
    00086
    00087     <b> Declarations:</b>
    00088
    00089     pass arguments explicitly:
    00090     \code
    00091     namespace vigra {
    00092         template <class SrcIterator, class SrcAccessor,
    00093                   class DestIterator, class DestAccessor>
    00094         void hourGlassFilter(SrcIterator sul, SrcIterator slr, SrcAccessor src,
    00095                              DestIterator dul, DestAccessor dest,
    00096                              double sigma, double rho);
    00097     }
    00098     \endcode
    00099
    00100
    00101     use argument objects in conjunction with \ref ArgumentObjectFactories:
    00102     \code
    00103     namespace vigra {
    00104         template <class SrcIterator, class SrcAccessor,
    00105                   class DestIterator, class DestAccessor>
    00106         inline
    00107         void hourGlassFilter(triple<SrcIterator, SrcIterator, SrcAccessor> s,
    00108                              pair<DestIterator, DestAccessor> d,
    00109                              double sigma, double rho);
    00110     }
    00111     \endcode
    00112
    00113     <b> Usage:</b>
    00114
    00115     <b>\#include</b> "<a href="orientedtensorfilters_8hxx-source.html">vigra/orientedtensorfilters.hxx</a>"
    00116
    00117     \code
    00118     FImage img(w,h);
    00119     FVector2Image gradient(w,h);
    00120     FVector3Image tensor(w,h), smoothedTensor(w,h);
    00121
    00122     gaussianGradient(srcImageRange(img), destImage(gradient), 1.0);
    00123     vectorToTensor(srcImageRange(gradient), destImage(tensor));
    00124     hourGlassFilter(srcImageRange(tensor), destImage(smoothedTensor), 2.0, 0.4);
    00125     \endcode
    00126
    00127     \see vectorToTensor()
    00128 */
    00129 template <class SrcIterator, class SrcAccessor,
    00130           class DestIterator, class DestAccessor>
    00131 void hourGlassFilter(SrcIterator sul, SrcIterator slr, SrcAccessor src,
    00132                      DestIterator dul, DestAccessor dest,
    00133                      double sigma, double rho)
    00134 {
    00135     vigra_precondition(sigma >= 0.0 && rho >= 0.0,
    00136                        "hourGlassFilter(): sigma and rho must be >= 0.0");
    00137     vigra_precondition(src.size(sul) == 3,
    00138                        "hourGlassFilter(): input image must have 3 bands.");
    00139     vigra_precondition(dest.size(dul) == 3,
    00140                        "hourGlassFilter(): output image must have 3 bands.");
    00141
    00142     // TODO: normalization
    00143
    00144     int w = slr.x - sul.x;
    00145     int h = slr.y - sul.y;
    00146
    00147     double radius = VIGRA_CSTD::floor(3.0*sigma + 0.5);
    00148     double sigma2 = -0.5 / sigma / sigma;
    00149     double rho2 = -0.5 / rho / rho;
    00150     double norm = 1.0 / (2.0 * M_PI * sigma * sigma);
    00151
    00152     initImage(dul, dul+Diff2D(w,h), dest, NumericTraits<typename DestAccessor::value_type>::zero());
    00153
    00154     for(int y=0; y<h; ++y, ++sul.y, ++dul.y)
    00155     {
    00156         SrcIterator s = sul;
    00157         DestIterator d = dul;
    00158         for(int x=0; x<w; ++x, ++s.x, ++d.x)
    00159         {
    00160             double phi = 0.5 * VIGRA_CSTD::atan2(
    00161                                      2.0*src.getComponent(s,1),
    00162                                      (double)src.getComponent(s,0) - src.getComponent(s,2));
    00163             double u = -VIGRA_CSTD::sin(phi);
    00164             double v = VIGRA_CSTD::cos(phi);
    00165
    00166             double x0 = x - radius < 0 ? -x : -radius;
    00167             double y0 = y - radius < 0 ? -y : -radius;
    00168             double x1 = x + radius >= w ? w - x - 1 : radius;
    00169             double y1 = y + radius >= h ? h - y - 1 : radius;
    00170
    00171             DestIterator dwul = d + Diff2D((int)x0, (int)y0);
    00172
    00173             for(double yy=y0; yy <= y1; ++yy, ++dwul.y)
    00174             {
    00175                 typename DestIterator::row_iterator dw = dwul.rowIterator();
    00176                 for(double xx=x0; xx <= x1; ++xx, ++dw)
    00177                 {
    00178                     double r2 = xx*xx + yy*yy;
    00179                     double p  = u*xx - v*yy;
    00180                     double q  = v*xx + u*yy;
    00181                     double kernel = (p == 0.0) ?
    00182                                       (q == 0.0) ?
    00183                                        norm :
    00184                                        0.0 :
    00185                                        norm * VIGRA_CSTD::exp(sigma2*r2 + rho2*q*q/p/p);
    00186                     dest.set(dest(dw) + kernel*src(s), dw);
    00187                 }
    00188             }
    00189         }
    00190     }
    00191 }
    00192
    00193 template <class SrcIterator, class SrcAccessor,
    00194           class DestIterator, class DestAccessor>
    00195 inline
    00196 void hourGlassFilter(triple<SrcIterator, SrcIterator, SrcAccessor> s,
    00197                      pair<DestIterator, DestAccessor> d,
    00198                      double sigma, double rho)
    00199 {
    00200     hourGlassFilter(s.first, s.second, s.third, d.first, d.second, sigma, rho);
    00201 }
    00202
    00203 /********************************************************/
    00204 /*                                                      */
    00205 /*                    ellipticGaussian                  */
    00206 /*                                                      */
    00207 /********************************************************/
    00208
    00209 template <class SrcIterator, class SrcAccessor,
    00210           class DestIterator, class DestAccessor>
    00211 void ellipticGaussian(SrcIterator sul, SrcIterator slr, SrcAccessor src,
    00212                       DestIterator dul, DestAccessor dest,
    00213                       double sigmax, double sigmin)
    00214 {
    00215     vigra_precondition(sigmax >= sigmin && sigmin >= 0.0,
    00216                        "ellipticGaussian(): "
    00217                        "sigmax >= sigmin and sigmin >= 0.0 required");
    00218
    00219     int w = slr.x - sul.x;
    00220     int h = slr.y - sul.y;
    00221
    00222     double radius = VIGRA_CSTD::floor(3.0*sigmax + 0.5);
    00223     double sigmin2 = -0.5 / sigmin / sigmin;
    00224     double norm = 1.0 / (2.0 * M_PI * sigmin * sigmax);
    00225
    00226     initImage(dul, dul+Diff2D(w,h), dest, NumericTraits<typename DestAccessor::value_type>::zero());
    00227
    00228     for(int y=0; y<h; ++y, ++sul.y, ++dul.y)
    00229     {
    00230         SrcIterator s = sul;
    00231         DestIterator d = dul;
    00232         for(int x=0; x<w; ++x, ++s.x, ++d.x)
    00233         {
    00234             typedef typename
    00235                NumericTraits<typename SrcAccessor::component_type>::RealPromote TmpType;
    00236             TmpType d1 = src.getComponent(s,0) + src.getComponent(s,2);
    00237             TmpType d2 = src.getComponent(s,0) - src.getComponent(s,2);
    00238             TmpType d3 = 2.0 * src.getComponent(s,1);
    00239             TmpType d4 = VIGRA_CSTD::sqrt(sq(d2) + sq(d3));
    00240             TmpType excentricity = 1.0 - (d1 - d4) / (d1 + d4);
    00241             double sigmax2 = -0.5 / sq((sigmax - sigmin)*excentricity + sigmin);
    00242
    00243             double phi = 0.5 * VIGRA_CSTD::atan2(d3, d2);
    00244             double u = -VIGRA_CSTD::sin(phi);
    00245             double v = VIGRA_CSTD::cos(phi);
    00246
    00247             double x0 = x - radius < 0 ? -x : -radius;
    00248             double y0 = y - radius < 0 ? -y : -radius;
    00249             double x1 = x + radius >= w ? w - x - 1 : radius;
    00250             double y1 = y + radius >= h ? h - y - 1 : radius;
    00251
    00252             DestIterator dwul = d + Diff2D((int)x0, (int)y0);
    00253
    00254             for(double yy=y0; yy <= y1; ++yy, ++dwul.y)
    00255             {
    00256                 typename DestIterator::row_iterator dw = dwul.rowIterator();
    00257                 for(double xx=x0; xx <= x1; ++xx, ++dw)
    00258                 {
    00259                     double p  = u*xx - v*yy;
    00260                     double q  = v*xx + u*yy;
    00261                     double kernel = norm * VIGRA_CSTD::exp(sigmax2*p*p + sigmin2*q*q);
    00262                     dest.set(dest(dw) + kernel*src(s), dw);
    00263                 }
    00264             }
    00265         }
    00266     }
    00267 }
    00268
    00269 template <class SrcIterator, class SrcAccessor,
    00270           class DestIterator, class DestAccessor>
    00271 inline
    00272 void ellipticGaussian(triple<SrcIterator, SrcIterator, SrcAccessor> s,
    00273                       pair<DestIterator, DestAccessor> d,
    00274                       double sigmax, double sigmin)
    00275 {
    00276     ellipticGaussian(s.first, s.second, s.third, d.first, d.second, sigmax, sigmin);
    00277 }
    00278
    00279 /********************************************************/
    00280 /*                                                      */
    00281 /*         kernels for orientedTrigonometricFilter      */
    00282 /*                                                      */
    00283 /********************************************************/
    00284
    00285 class FoerstnerKernelBase
    00286 {
    00287   public:
    00288     typedef double ResultType;
    00289     typedef double WeightType;
    00290     typedef DVector2Image::value_type VectorType;
    00291
    00292     FoerstnerKernelBase(double scale, bool ringShaped = false)
    00293     : radius_((int)(3.0*scale+0.5)),
    00294       weights_(2*radius_+1, 2*radius_+1),
    00295       vectors_(2*radius_+1, 2*radius_+1)
    00296     {
    00297         double norm = 1.0 / (2.0 * M_PI * scale * scale);
    00298         double s2 = -0.5 / scale / scale;
    00299
    00300         for(int y = -radius_; y <= radius_; ++y)
    00301         {
    00302             for(int x = -radius_; x <= radius_; ++x)
    00303             {
    00304                 double d2 = x*x + y*y;
    00305                 double d = VIGRA_CSTD::sqrt(d2);
    00306                 vectors_(x+radius_,y+radius_) = d != 0.0 ?
    00307                                                   VectorType(x/d, -y/d) :
    00308                                                   VectorType(0, 0);
    00309                 weights_(x+radius_,y+radius_) = ringShaped ?
    00310                                        norm * d2 * VIGRA_CSTD::exp(d2 * s2) :
    00311                                        norm * VIGRA_CSTD::exp(d2 * s2);
    00312             }
    00313         }
    00314     }
    00315
    00316     ResultType operator()(int x, int y, VectorType const &) const
    00317     {
    00318         // isotropic filtering
    00319         return weights_(radius_, radius_);
    00320     }
    00321
    00322     int radius_;
    00323     DImage weights_;
    00324     DVector2Image vectors_;
    00325 };
    00326
    00327 class FoerstnerRingKernelBase
    00328 : public FoerstnerKernelBase
    00329 {
    00330   public:
    00331     FoerstnerRingKernelBase(double scale)
    00332     : FoerstnerKernelBase(scale, true)
    00333     {}
    00334 };
    00335
    00336 class Cos2RingKernel
    00337 : public FoerstnerKernelBase
    00338 {
    00339   public:
    00340     typedef double ResultType;
    00341     typedef double WeightType;
    00342     typedef DVector2Image::value_type VectorType;
    00343
    00344     Cos2RingKernel(double scale)
    00345     : FoerstnerKernelBase(scale, true)
    00346     {}
    00347
    00348     ResultType operator()(int x, int y, VectorType const & v) const
    00349     {
    00350         if(x == 0 && y == 0)
    00351             return weights_(radius_, radius_);
    00352         double d = dot(vectors_(x+radius_, y+radius_), v);
    00353         return d * d * weights_(x+radius_, y+radius_);
    00354     }
    00355 };
    00356
    00357 class Cos2Kernel
    00358 : public FoerstnerKernelBase
    00359 {
    00360   public:
    00361     typedef double ResultType;
    00362     typedef double WeightType;
    00363     typedef DVector2Image::value_type VectorType;
    00364
    00365     Cos2Kernel(double scale)
    00366     : FoerstnerKernelBase(scale, false)
    00367     {}
    00368
    00369     ResultType operator()(int x, int y, VectorType const & v) const
    00370     {
    00371         if(x == 0 && y == 0)
    00372             return weights_(radius_, radius_);
    00373         double d = dot(vectors_(x+radius_, y+radius_), v);
    00374         return d * d * weights_(x+radius_, y+radius_);
    00375     }
    00376 };
    00377
    00378 class Sin2RingKernel
    00379 : public FoerstnerKernelBase
    00380 {
    00381   public:
    00382     typedef double ResultType;
    00383     typedef double WeightType;
    00384     typedef DVector2Image::value_type VectorType;
    00385
    00386     Sin2RingKernel(double scale)
    00387     : FoerstnerKernelBase(scale, true)
    00388     {}
    00389
    00390     ResultType operator()(int x, int y, VectorType const & v) const
    00391     {
    00392         if(x == 0 && y == 0)
    00393             return weights_(radius_, radius_);
    00394         double d = dot(vectors_(x+radius_, y+radius_), v);
    00395         return (1.0 - d * d) * weights_(x+radius_, y+radius_);
    00396     }
    00397 };
    00398
    00399 class Sin2Kernel
    00400 : public FoerstnerKernelBase
    00401 {
    00402   public:
    00403     typedef double ResultType;
    00404     typedef double WeightType;
    00405     typedef DVector2Image::value_type VectorType;
    00406
    00407     Sin2Kernel(double scale)
    00408     : FoerstnerKernelBase(scale, false)
    00409     {}
    00410
    00411     ResultType operator()(int x, int y, VectorType const & v) const
    00412     {
    00413         if(x == 0 && y == 0)
    00414             return weights_(radius_, radius_);
    00415         double d = dot(vectors_(x+radius_, y+radius_), v);
    00416         return (1.0 - d * d) * weights_(x+radius_, y+radius_);
    00417     }
    00418 };
    00419
    00420 class Sin6RingKernel
    00421 : public FoerstnerKernelBase
    00422 {
    00423   public:
    00424     typedef double ResultType;
    00425     typedef double WeightType;
    00426     typedef DVector2Image::value_type VectorType;
    00427
    00428     Sin6RingKernel(double scale)
    00429     : FoerstnerKernelBase(scale, true)
    00430     {}
    00431
    00432     ResultType operator()(int x, int y, VectorType const & v) const
    00433     {
    00434         if(x == 0 && y == 0)
    00435             return weights_(radius_, radius_);
    00436         double d = dot(vectors_(x+radius_, y+radius_), v);
    00437         return VIGRA_CSTD::pow(1.0 - d * d, 3) * weights_(x+radius_, y+radius_);
    00438     }
    00439 };
    00440
    00441 class Sin6Kernel
    00442 : public FoerstnerKernelBase
    00443 {
    00444   public:
    00445     typedef double ResultType;
    00446     typedef double WeightType;
    00447     typedef DVector2Image::value_type VectorType;
    00448
    00449     Sin6Kernel(double scale)
    00450     : FoerstnerKernelBase(scale, false)
    00451     {}
    00452
    00453     ResultType operator()(int x, int y, VectorType const & v) const
    00454     {
    00455         if(x == 0 && y == 0)
    00456             return weights_(radius_, radius_);
    00457         double d = dot(vectors_(x+radius_, y+radius_), v);
    00458         return VIGRA_CSTD::pow(1.0 - d * d, 3) * weights_(x+radius_, y+radius_);
    00459     }
    00460 };
    00461
    00462 class Cos6RingKernel
    00463 : public FoerstnerKernelBase
    00464 {
    00465   public:
    00466     typedef double ResultType;
    00467     typedef double WeightType;
    00468     typedef DVector2Image::value_type VectorType;
    00469
    00470     Cos6RingKernel(double scale)
    00471     : FoerstnerKernelBase(scale, true)
    00472     {}
    00473
    00474     ResultType operator()(int x, int y, VectorType const & v) const
    00475     {
    00476         if(x == 0 && y == 0)
    00477             return weights_(radius_, radius_);
    00478         double d = dot(vectors_(x+radius_, y+radius_), v);
    00479         return (1.0 - VIGRA_CSTD::pow(1.0 - d * d, 3)) * weights_(x+radius_, y+radius_);
    00480     }
    00481 };
    00482
    00483 class Cos6Kernel
    00484 : public FoerstnerKernelBase
    00485 {
    00486   public:
    00487     typedef double ResultType;
    00488     typedef double WeightType;
    00489     typedef DVector2Image::value_type VectorType;
    00490
    00491     Cos6Kernel(double scale)
    00492     : FoerstnerKernelBase(scale, false)
    00493     {}
    00494
    00495     ResultType operator()(int x, int y, VectorType const & v) const
    00496     {
    00497         if(x == 0 && y == 0)
    00498             return weights_(radius_, radius_);
    00499         double d = dot(vectors_(x+radius_, y+radius_), v);
    00500         return (1.0 - VIGRA_CSTD::pow(1.0 - d * d, 3)) * weights_(x+radius_, y+radius_);
    00501     }
    00502 };
    00503
    00504 /********************************************************/
    00505 /*                                                      */
    00506 /*              orientedTrigonometricFilter             */
    00507 /*                                                      */
    00508 /********************************************************/
    00509
    00510 template <class SrcIterator, class SrcAccessor,
    00511           class DestIterator, class DestAccessor,
    00512           class Kernel>
    00513 void orientedTrigonometricFilter(SrcIterator sul, SrcIterator slr, SrcAccessor src,
    00514                     DestIterator dul, DestAccessor dest,
    00515                     Kernel const & kernel)
    00516 {
    00517     vigra_precondition(src.size(sul) == 2,
    00518                        "orientedTrigonometricFilter(): input image must have 2 bands.");
    00519     vigra_precondition(dest.size(dul) == 3,
    00520                        "orientedTrigonometricFilter(): output image must have 3 bands.");
    00521
    00522     int w = slr.x - sul.x;
    00523     int h = slr.y - sul.y;
    00524     int radius = kernel.radius_;
    00525
    00526     typedef typename SrcAccessor::value_type VectorType;
    00527     typedef typename DestAccessor::value_type TensorType;
    00528
    00529     initImage(dul, dul+Diff2D(w,h), dest, NumericTraits<TensorType>::zero());
    00530
    00531     for(int y=0; y<h; ++y, ++sul.y, ++dul.y)
    00532     {
    00533         SrcIterator s = sul;
    00534         DestIterator d = dul;
    00535         for(int x=0; x<w; ++x, ++s.x, ++d.x)
    00536         {
    00537             int x0 = x - radius < 0 ? -x : -radius;
    00538             int y0 = y - radius < 0 ? -y : -radius;
    00539             int x1 = x + radius >= w ? w - x - 1 : radius;
    00540             int y1 = y + radius >= h ? h - y - 1 : radius;
    00541
    00542             VectorType v(src(s));
    00543             TensorType t(sq(v[0]), v[0]*v[1], sq(v[1]));
    00544             double sqMag = t[0] + t[2];
    00545             double mag = VIGRA_CSTD::sqrt(sqMag);
    00546             if(mag != 0.0)
    00547                 v /= mag;
    00548             else
    00549                 v *= 0.0;
    00550             Diff2D dd;
    00551             for(dd.y = y0; dd.y <= y1; ++dd.y)
    00552             {
    00553                 for(dd.x = x0; dd.x <= x1; ++dd.x)
    00554                 {
    00555                     dest.set(dest(d, dd) + kernel(dd.x, dd.y, v) * t, d, dd);
    00556                 }
    00557             }
    00558         }
    00559     }
    00560 }
    00561
    00562 template <class SrcIterator, class SrcAccessor,
    00563           class DestIterator, class DestAccessor,
    00564           class Kernel>
    00565 inline
    00566 void orientedTrigonometricFilter(triple<SrcIterator, SrcIterator, SrcAccessor> s,
    00567                       pair<DestIterator, DestAccessor> d,
    00568                       Kernel const & kernel)
    00569 {
    00570     orientedTrigonometricFilter(s.first, s.second, s.third, d.first, d.second, kernel);
    00571 }
    00572
    00573 //@}
    00574
    00575 } // namespace vigra
    00576
    00577 #endif /* VIGRA_ORIENTEDTENSORFILTERS_HXX */

© Ullrich Köthe (koethe@informatik.uni-hamburg.de) Cognitive Systems Group, University of Hamburg, Germany | html generated using doxygen and Python VIGRA 1.5.0 (7 Dec 2006)