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    00001 /************************************************************************/
    00002 /*                                                                      */
    00003 /*               Copyright 2002-2004 by Ullrich Koethe                  */
    00004 /*                                                                      */
    00005 /*    This file is part of the VIGRA computer vision library.           */
    00006 /*    The VIGRA Website is                                              */
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    00009 /*        ullrich.koethe@iwr.uni-heidelberg.de    or                    */
    00010 /*        vigra@informatik.uni-hamburg.de                               */
    00011 /*                                                                      */
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    00023 /*    Software.                                                         */
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    00033 /*                                                                      */
    00034 /************************************************************************/
    00035
    00036 #ifndef VIGRA_ORIENTEDTENSORFILTERS_HXX
    00037 #define VIGRA_ORIENTEDTENSORFILTERS_HXX
    00038
    00039 #include <cmath>
    00040 #include "utilities.hxx"
    00041 #include "initimage.hxx"
    00042 #include "stdconvolution.hxx"
    00043
    00044 namespace vigra {
    00045
    00046 /** \addtogroup TensorImaging Tensor Image Processing
    00047 */
    00048 //@{
    00049
    00050 /********************************************************/
    00051 /*                                                      */
    00052 /*                     hourGlassFilter                  */
    00053 /*                                                      */
    00054 /********************************************************/
    00055
    00056 /** \brief Anisotropic tensor smoothing with the hourglass filter.
    00057
    00058     This function implements anisotropic tensor smoothing by an
    00059     hourglass-shaped filters as described in
    00060
    00061     U. K&ouml;the: <a href="http://hci.iwr.uni-heidelberg.de/people/ukoethe/papers/index.php#cite_structureTensor">
    00062     <i>"Edge and Junction Detection with an Improved Structure Tensor"</i></a>,
    00063      in: Proc. of 25th DAGM Symposium, Magdeburg 2003, Lecture Notes in Computer Science 2781,
    00064      pp. 25-32, Heidelberg: Springer, 2003
    00065
    00066     It is closely related to the structure tensor (see \ref structureTensor()), but
    00067     replaces the linear tensor smoothing with a smoothing along edges only.
    00068     Smoothing accross edges is largely suppressed. This means that the
    00069     image structure is preserved much better because nearby features
    00070     such as parallel edges are not blended into each other.
    00071
    00072     The hourglass filter is typically applied to a gradient tensor, i.e. the
    00073     Euclidean product of the gradient with itself, which can be obtained by a
    00074     gradient operator followed with \ref vectorToTensor(), see example below.
    00075     The hourglass shape of the filter can be interpreted as indicating the likely
    00076     continuations of a local edge element. The parameter <tt>sigma</tt> determines
    00077     the radius of the hourglass (i.e. how far the influence of the edge element
    00078     reaches), and <tt>rho</tt> controls its opening angle (i.e. how narrow the
    00079     edge orientation os followed). Recommended values are <tt>sigma = 1.4</tt>
    00080     (or, more generally, two to three times the scale of the gradient operator
    00081     used in the first step), and <tt>rho = 0.4</tt> which corresponds to an
    00082     opening angle of 22.5 degrees to either side of the edge.
    00083
    00084     <b> Declarations:</b>
    00085
    00086     pass arguments explicitly:
    00087     \code
    00088     namespace vigra {
    00089         template <class SrcIterator, class SrcAccessor,
    00090                   class DestIterator, class DestAccessor>
    00091         void hourGlassFilter(SrcIterator sul, SrcIterator slr, SrcAccessor src,
    00092                              DestIterator dul, DestAccessor dest,
    00093                              double sigma, double rho);
    00094     }
    00095     \endcode
    00096
    00097
    00098     use argument objects in conjunction with \ref ArgumentObjectFactories :
    00099     \code
    00100     namespace vigra {
    00101         template <class SrcIterator, class SrcAccessor,
    00102                   class DestIterator, class DestAccessor>
    00103         inline
    00104         void hourGlassFilter(triple<SrcIterator, SrcIterator, SrcAccessor> s,
    00105                              pair<DestIterator, DestAccessor> d,
    00106                              double sigma, double rho);
    00107     }
    00108     \endcode
    00109
    00110     <b> Usage:</b>
    00111
    00112     <b>\#include</b> <<a href="orientedtensorfilters_8hxx-source.html">vigra/orientedtensorfilters.hxx</a>>
    00113
    00114     \code
    00115     FImage img(w,h);
    00116     FVector2Image gradient(w,h);
    00117     FVector3Image tensor(w,h), smoothedTensor(w,h);
    00118
    00119     gaussianGradient(srcImageRange(img), destImage(gradient), 1.0);
    00120     vectorToTensor(srcImageRange(gradient), destImage(tensor));
    00121     hourGlassFilter(srcImageRange(tensor), destImage(smoothedTensor), 2.0, 0.4);
    00122     \endcode
    00123
    00124     \see vectorToTensor()
    00125 */
    00126 doxygen_overloaded_function(template <...> void hourGlassFilter)
    00127
    00128 template <class SrcIterator, class SrcAccessor,
    00129           class DestIterator, class DestAccessor>
    00130 void hourGlassFilter(SrcIterator sul, SrcIterator slr, SrcAccessor src,
    00131                      DestIterator dul, DestAccessor dest,
    00132                      double sigma, double rho)
    00133 {
    00134     vigra_precondition(sigma >= 0.0 && rho >= 0.0,
    00135                        "hourGlassFilter(): sigma and rho must be >= 0.0");
    00136     vigra_precondition(src.size(sul) == 3,
    00137                        "hourGlassFilter(): input image must have 3 bands.");
    00138     vigra_precondition(dest.size(dul) == 3,
    00139                        "hourGlassFilter(): output image must have 3 bands.");
    00140
    00141     // TODO: normalization
    00142
    00143     int w = slr.x - sul.x;
    00144     int h = slr.y - sul.y;
    00145
    00146     double radius = VIGRA_CSTD::floor(3.0*sigma + 0.5);
    00147     double sigma2 = -0.5 / sigma / sigma;
    00148     double rho2 = -0.5 / rho / rho;
    00149     double norm = 1.0 / (2.0 * M_PI * sigma * sigma);
    00150
    00151     initImage(dul, dul+Diff2D(w,h), dest, NumericTraits<typename DestAccessor::value_type>::zero());
    00152
    00153     for(int y=0; y<h; ++y, ++sul.y, ++dul.y)
    00154     {
    00155         SrcIterator s = sul;
    00156         DestIterator d = dul;
    00157         for(int x=0; x<w; ++x, ++s.x, ++d.x)
    00158         {
    00159             double phi = 0.5 * VIGRA_CSTD::atan2(
    00160                                      2.0*src.getComponent(s,1),
    00161                                      (double)src.getComponent(s,0) - src.getComponent(s,2));
    00162             double u = VIGRA_CSTD::sin(phi);
    00163             double v = VIGRA_CSTD::cos(phi);
    00164
    00165             double x0 = x - radius < 0 ? -x : -radius;
    00166             double y0 = y - radius < 0 ? -y : -radius;
    00167             double x1 = x + radius >= w ? w - x - 1 : radius;
    00168             double y1 = y + radius >= h ? h - y - 1 : radius;
    00169
    00170             DestIterator dwul = d + Diff2D((int)x0, (int)y0);
    00171
    00172             for(double yy=y0; yy <= y1; ++yy, ++dwul.y)
    00173             {
    00174                 typename DestIterator::row_iterator dw = dwul.rowIterator();
    00175                 for(double xx=x0; xx <= x1; ++xx, ++dw)
    00176                 {
    00177                     double r2 = xx*xx + yy*yy;
    00178                     double p  = u*xx - v*yy;
    00179                     double q  = v*xx + u*yy;
    00180                     double kernel = (p == 0.0) ?
    00181                                       (q == 0.0) ?
    00182                                        norm :
    00183                                        0.0 :
    00184                                        norm * VIGRA_CSTD::exp(sigma2*r2 + rho2*q*q/p/p);
    00185                     dest.set(dest(dw) + kernel*src(s), dw);
    00186                 }
    00187             }
    00188         }
    00189     }
    00190 }
    00191
    00192 template <class SrcIterator, class SrcAccessor,
    00193           class DestIterator, class DestAccessor>
    00194 inline
    00195 void hourGlassFilter(triple<SrcIterator, SrcIterator, SrcAccessor> s,
    00196                      pair<DestIterator, DestAccessor> d,
    00197                      double sigma, double rho)
    00198 {
    00199     hourGlassFilter(s.first, s.second, s.third, d.first, d.second, sigma, rho);
    00200 }
    00201
    00202 /********************************************************/
    00203 /*                                                      */
    00204 /*                    ellipticGaussian                  */
    00205 /*                                                      */
    00206 /********************************************************/
    00207
    00208 template <class SrcIterator, class SrcAccessor,
    00209           class DestIterator, class DestAccessor>
    00210 void ellipticGaussian(SrcIterator sul, SrcIterator slr, SrcAccessor src,
    00211                       DestIterator dul, DestAccessor dest,
    00212                       double sigmax, double sigmin)
    00213 {
    00214     vigra_precondition(sigmax >= sigmin && sigmin >= 0.0,
    00215                        "ellipticGaussian(): "
    00216                        "sigmax >= sigmin and sigmin >= 0.0 required");
    00217
    00218     int w = slr.x - sul.x;
    00219     int h = slr.y - sul.y;
    00220
    00221     double radius = VIGRA_CSTD::floor(3.0*sigmax + 0.5);
    00222     double sigmin2 = -0.5 / sigmin / sigmin;
    00223     double norm = 1.0 / (2.0 * M_PI * sigmin * sigmax);
    00224
    00225     initImage(dul, dul+Diff2D(w,h), dest, NumericTraits<typename DestAccessor::value_type>::zero());
    00226
    00227     for(int y=0; y<h; ++y, ++sul.y, ++dul.y)
    00228     {
    00229         SrcIterator s = sul;
    00230         DestIterator d = dul;
    00231         for(int x=0; x<w; ++x, ++s.x, ++d.x)
    00232         {
    00233             typedef typename
    00234                NumericTraits<typename SrcAccessor::component_type>::RealPromote TmpType;
    00235             TmpType d1 = src.getComponent(s,0) + src.getComponent(s,2);
    00236             TmpType d2 = src.getComponent(s,0) - src.getComponent(s,2);
    00237             TmpType d3 = 2.0 * src.getComponent(s,1);
    00238             TmpType d4 = VIGRA_CSTD::sqrt(sq(d2) + sq(d3));
    00239             TmpType excentricity = 1.0 - (d1 - d4) / (d1 + d4);
    00240             double sigmax2 = -0.5 / sq((sigmax - sigmin)*excentricity + sigmin);
    00241
    00242             double phi = 0.5 * VIGRA_CSTD::atan2(d3, d2);
    00243             double u = VIGRA_CSTD::sin(phi);
    00244             double v = VIGRA_CSTD::cos(phi);
    00245
    00246             double x0 = x - radius < 0 ? -x : -radius;
    00247             double y0 = y - radius < 0 ? -y : -radius;
    00248             double x1 = x + radius >= w ? w - x - 1 : radius;
    00249             double y1 = y + radius >= h ? h - y - 1 : radius;
    00250
    00251             DestIterator dwul = d + Diff2D((int)x0, (int)y0);
    00252
    00253             for(double yy=y0; yy <= y1; ++yy, ++dwul.y)
    00254             {
    00255                 typename DestIterator::row_iterator dw = dwul.rowIterator();
    00256                 for(double xx=x0; xx <= x1; ++xx, ++dw)
    00257                 {
    00258                     double p  = u*xx - v*yy;
    00259                     double q  = v*xx + u*yy;
    00260                     double kernel = norm * VIGRA_CSTD::exp(sigmax2*p*p + sigmin2*q*q);
    00261                     dest.set(dest(dw) + kernel*src(s), dw);
    00262                 }
    00263             }
    00264         }
    00265     }
    00266 }
    00267
    00268 template <class SrcIterator, class SrcAccessor,
    00269           class DestIterator, class DestAccessor>
    00270 inline
    00271 void ellipticGaussian(triple<SrcIterator, SrcIterator, SrcAccessor> s,
    00272                       pair<DestIterator, DestAccessor> d,
    00273                       double sigmax, double sigmin)
    00274 {
    00275     ellipticGaussian(s.first, s.second, s.third, d.first, d.second, sigmax, sigmin);
    00276 }
    00277
    00278 /********************************************************/
    00279 /*                                                      */
    00280 /*         kernels for orientedTrigonometricFilter      */
    00281 /*                                                      */
    00282 /********************************************************/
    00283
    00284 class FoerstnerKernelBase
    00285 {
    00286   public:
    00287     typedef double ResultType;
    00288     typedef double WeightType;
    00289     typedef DVector2Image::value_type VectorType;
    00290     typedef VectorType::value_type    ValueType;
    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(ValueType(0), ValueType(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 (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.7.1 (3 Dec 2010)