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multi_watersheds.hxx
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35
36#ifndef VIGRA_MULTI_WATERSHEDS_HXX
37#define VIGRA_MULTI_WATERSHEDS_HXX
38
39#include <functional>
40#include <limits>
41#include "mathutil.hxx"
42#include "multi_array.hxx"
43#include "multi_math.hxx"
44#include "multi_gridgraph.hxx"
45#include "multi_localminmax.hxx"
46#include "multi_labeling.hxx"
47#include "watersheds.hxx"
48#include "bucket_queue.hxx"
49#include "union_find.hxx"
50
51 namespace vigra {
52
53/** \addtogroup Superpixels
54*/
55//@{
56 namespace lemon_graph {
57
58 namespace graph_detail {
59
60 // select the neighbor ID for union-find watersheds
61 // standard behavior: use global node ID
62 template <class Graph>
63 struct NeighborIndexFunctor
64{
65 typedef typename Graph::index_type index_type;
66
67 template <class NodeIter, class ArcIter>
68 static index_type get(Graph const & g, NodeIter const &, ArcIter const & a)
69 {
70 return g.id(g.target(*a));
71 }
72
73 template <class NodeIter, class ArcIter>
74 static index_type getOpposite(Graph const & g, NodeIter const & n, ArcIter const &)
75 {
76 return g.id(*n);
77 }
78
79 static index_type invalidIndex(Graph const &)
80 {
81 return std::numeric_limits<index_type>::max();
82 }
83};
84
85 // select the neighbor ID for union-find watersheds
86 // GridGraph optimization: use local neighbor index (needs only 1/4 of the memory)
87 template<unsigned int N, class DirectedTag>
88 struct NeighborIndexFunctor<GridGraph<N, DirectedTag> >
89{
90 typedef GridGraph<N, DirectedTag> Graph;
91 typedef UInt16 index_type;
92
93 template <class NodeIter, class ArcIter>
94 static index_type get(Graph const &, NodeIter const &, ArcIter const & a)
95 {
96 return a.neighborIndex();
97 }
98
99 template <class NodeIter, class ArcIter>
100 static index_type getOpposite(Graph const & g, NodeIter const &, ArcIter const & a)
101 {
102 return g.oppositeIndex(a.neighborIndex());
103 }
104 static index_type invalidIndex(Graph const &)
105 {
106 return std::numeric_limits<index_type>::max();
107 }
108};
109
110 template <class Graph, class T1Map, class T2Map>
111 void
112prepareWatersheds(Graph const & g,
113 T1Map const & data,
114 T2Map & lowestNeighborIndex)
115{
116 typedef typename Graph::NodeIt graph_scanner;
117 typedef typename Graph::OutArcIt neighbor_iterator;
118 typedef NeighborIndexFunctor<Graph> IndexFunctor;
119
120 for (graph_scanner node(g); node != INVALID; ++node)
121 {
122 typename T1Map::value_type lowestValue = data[*node];
123 typename T2Map::value_type lowestIndex = IndexFunctor::invalidIndex(g);
124
125 for(neighbor_iterator arc(g, *node); arc != INVALID; ++arc)
126 {
127 if(data[g.target(*arc)] < lowestValue)
128 {
129 lowestValue = data[g.target(*arc)];
130 lowestIndex = IndexFunctor::get(g, node, arc);
131 }
132 }
133 lowestNeighborIndex[*node] = lowestIndex;
134 }
135}
136
137
138 template <class Graph, class T1Map, class T2Map, class T3Map>
139 typename T2Map::value_type
140unionFindWatersheds(Graph const & g,
141 T1Map const &,
142 T2Map const & lowestNeighborIndex,
143 T3Map & labels)
144{
145 typedef typename Graph::NodeIt graph_scanner;
146 typedef typename Graph::OutBackArcIt neighbor_iterator;
147 typedef typename T3Map::value_type LabelType;
148 typedef NeighborIndexFunctor<Graph> IndexFunctor;
149
150 vigra::UnionFindArray<LabelType> regions;
151
152 // pass 1: find connected components
153 for (graph_scanner node(g); node != INVALID; ++node)
154 {
155 // define tentative label for current node
156 LabelType currentIndex = regions.nextFreeIndex();
157
158 for (neighbor_iterator arc(g, node); arc != INVALID; ++arc)
159 {
160 // merge regions if current target is center's lowest neighbor or vice versa
161 if((lowestNeighborIndex[*node] == IndexFunctor::invalidIndex(g) &&
162 lowestNeighborIndex[g.target(*arc)] == IndexFunctor::invalidIndex(g)) ||
163 (lowestNeighborIndex[*node] == IndexFunctor::get(g, node, arc)) ||
164 (lowestNeighborIndex[g.target(*arc)] == IndexFunctor::getOpposite(g, node, arc)))
165 {
166 currentIndex = regions.makeUnion(labels[g.target(*arc)], currentIndex);
167 }
168 }
169
170 // set label of current node
171 labels[*node] = regions.finalizeIndex(currentIndex);
172 }
173
174 LabelType count = regions.makeContiguous();
175
176 // pass 2: make component labels contiguous
177 for (graph_scanner node(g); node != INVALID; ++node)
178 {
179 labels[*node] = regions.findLabel(labels[*node]);
180 }
181 return count;
182}
183
184 template <class Graph, class T1Map, class T2Map>
185 typename T2Map::value_type
186generateWatershedSeeds(Graph const & g,
187 T1Map const & data,
188 T2Map & seeds,
189 SeedOptions const & options = SeedOptions())
190{
191 typedef typename T1Map::value_type DataType;
192 typedef unsigned char MarkerType;
193
194 typename Graph::template NodeMap<MarkerType> minima(g);
195
196 if(options.mini == SeedOptions::LevelSets)
197 {
198 vigra_precondition(options.thresholdIsValid<DataType>(),
199 "generateWatershedSeeds(): SeedOptions.levelSets() must be specified with threshold.");
200
201 using namespace multi_math;
202 for(typename Graph::NodeIt iter(g);iter!=lemon::INVALID;++iter){
203 minima[*iter]= data[*iter] <= DataType(options.thresh);
204 }
205 }
206 else
207 {
208 DataType threshold = options.thresholdIsValid<DataType>()
209 ? options.thresh
210 : NumericTraits<DataType>::max();
211
212 if(options.mini == SeedOptions::ExtendedMinima)
213 extendedLocalMinMaxGraph(g, data, minima, MarkerType(1), threshold,
214 std::less<DataType>(), std::equal_to<DataType>(), true);
215 else
216 lemon_graph::localMinMaxGraph(g, data, minima, MarkerType(1), threshold,
217 std::less<DataType>(), true);
218 }
219 return labelGraphWithBackground(g, minima, seeds, MarkerType(0), std::equal_to<MarkerType>());
220}
221
222#ifdef __GNUC__
223#pragma GCC diagnostic push
224#pragma GCC diagnostic ignored "-Wsign-compare"
225#endif
226
227 template <class Graph, class T1Map, class T2Map>
228 typename T2Map::value_type
229seededWatersheds(Graph const & g,
230 T1Map const & data,
231 T2Map & labels,
232 WatershedOptions const & options)
233{
234 typedef typename Graph::Node Node;
235 typedef typename Graph::NodeIt graph_scanner;
236 typedef typename Graph::OutArcIt neighbor_iterator;
237 typedef typename T1Map::value_type CostType;
238 typedef typename T2Map::value_type LabelType;
239
240 PriorityQueue<Node, CostType, true> pqueue;
241
242 bool keepContours = ((options.terminate & KeepContours) != 0);
243 LabelType maxRegionLabel = 0;
244
245 for (graph_scanner node(g); node != INVALID; ++node)
246 {
247 LabelType label = labels[*node];
248 if(label != 0)
249 {
250 if(maxRegionLabel < label)
251 maxRegionLabel = label;
252
253 for (neighbor_iterator arc(g, *node); arc != INVALID; ++arc)
254 {
255 if(labels[g.target(*arc)] == 0)
256 {
257 // register all seeds that have an unlabeled neighbor
258 if(label == options.biased_label)
259 pqueue.push(*node, data[*node] * options.bias);
260 else
261 pqueue.push(*node, data[*node]);
262 break;
263 }
264 }
265 }
266 }
267
268 LabelType contourLabel = maxRegionLabel + 1; // temporary contour label
269
270 // perform region growing
271 while(!pqueue.empty())
272 {
273 Node node = pqueue.top();
274 CostType cost = pqueue.topPriority();
275 pqueue.pop();
276
277 if((options.terminate & StopAtThreshold) && (cost > options.max_cost))
278 break;
279
280 LabelType label = labels[node];
281
282 if(label == contourLabel)
283 continue;
284
285 // Put the unlabeled neighbors in the priority queue.
286 for (neighbor_iterator arc(g, node); arc != INVALID; ++arc)
287 {
288 LabelType neighborLabel = labels[g.target(*arc)];
289 if(neighborLabel == 0)
290 {
291 labels[g.target(*arc)] = label;
292 CostType priority = (label == options.biased_label)
293 ? data[g.target(*arc)] * options.bias
294 : data[g.target(*arc)];
295 if(priority < cost)
296 priority = cost;
297 pqueue.push(g.target(*arc), priority);
298 }
299 else if(keepContours && (label != neighborLabel) && (neighborLabel != contourLabel))
300 {
301 // The present neighbor is adjacent to more than one region
302 // => mark it as contour.
303 CostType priority = (neighborLabel == options.biased_label)
304 ? data[g.target(*arc)] * options.bias
305 : data[g.target(*arc)];
306 if(cost < priority) // neighbor not yet processed
307 labels[g.target(*arc)] = contourLabel;
308 }
309 }
310 }
311
312 if(keepContours)
313 {
314 // Replace the temporary contour label with label 0.
315 ///typename T2Map::iterator k = labels.begin(),
316 /// end = labels.end();
317 ///for(; k != end; ++k)
318 /// if(*k == contourLabel)
319 /// *k = 0;
320
321 for(typename Graph::NodeIt iter(g);iter!=lemon::INVALID;++iter){
322 if(labels[*iter]==contourLabel)
323 labels[*iter]=0;
324 }
325 }
326
327 return maxRegionLabel;
328}
329
330#ifdef __GNUC__
331#pragma GCC diagnostic pop
332#endif
333
334} // namespace graph_detail
335
336 template <class Graph, class T1Map, class T2Map>
337 typename T2Map::value_type
338watershedsGraph(Graph const & g,
339 T1Map const & data,
340 T2Map & labels,
341 WatershedOptions const & options)
342{
343 if(options.method == WatershedOptions::UnionFind)
344 {
345 typedef typename graph_detail::NeighborIndexFunctor<Graph>::index_type index_type;
346
347 vigra_precondition((index_type)g.maxDegree() <= NumericTraits<index_type>::max(),
348 "watershedsGraph(): cannot handle nodes with degree > 65535.");
349
350 typename Graph::template NodeMap<index_type> lowestNeighborIndex(g);
351
352 graph_detail::prepareWatersheds(g, data, lowestNeighborIndex);
353 return graph_detail::unionFindWatersheds(g, data, lowestNeighborIndex, labels);
354 }
355 else if(options.method == WatershedOptions::RegionGrowing)
356 {
357 SeedOptions seed_options;
358
359 // check if the user has explicitly requested seed computation
360 if(options.seed_options.mini != SeedOptions::Unspecified)
361 {
362 seed_options = options.seed_options;
363 }
364 else
365 {
366 // otherwise, don't compute seeds if 'labels' already contains them
367 if(labels.any())
368 seed_options.mini = SeedOptions::Unspecified;
369 }
370
371 if(seed_options.mini != SeedOptions::Unspecified)
372 {
373 graph_detail::generateWatershedSeeds(g, data, labels, seed_options);
374 }
375
376 return graph_detail::seededWatersheds(g, data, labels, options);
377 }
378 else
379 {
380 vigra_precondition(false,
381 "watershedsGraph(): invalid method in watershed options.");
382 return 0;
383 }
384}
385
386
387} // namespace lemon_graph
388
389 // documentation is in watersheds.hxx
390 template <unsigned int N, class T, class S1,
391 class Label, class S2>
392 inline Label
393generateWatershedSeeds(MultiArrayView<N, T, S1> const & data,
394 MultiArrayView<N, Label, S2> seeds,
395 NeighborhoodType neighborhood = IndirectNeighborhood,
396 SeedOptions const & options = SeedOptions())
397{
398 vigra_precondition(data.shape() == seeds.shape(),
399 "generateWatershedSeeds(): Shape mismatch between input and output.");
400
401 GridGraph<N, undirected_tag> graph(data.shape(), neighborhood);
402 return lemon_graph::graph_detail::generateWatershedSeeds(graph, data, seeds, options);
403}
404
405
406/** \brief Watershed segmentation of an arbitrary-dimensional array.
407
408 See also \ref unionFindWatershedsBlockwise() for a parallel version of the
409 watershed algorithm.
410
411 This function implements variants of the watershed algorithms
412 described in
413
414 [1] L. Vincent and P. Soille: <em>"Watersheds in digital spaces: An efficient algorithm
415 based on immersion simulations"</em>, IEEE Trans. Patt. Analysis Mach. Intell. 13(6):583-598, 1991
416
417 [2] J. Roerdink, R. Meijster: <em>"The watershed transform: definitions, algorithms,
418 and parallelization strategies"</em>, Fundamenta Informaticae, 41:187-228, 2000
419
420 The source array \a data is a boundary indicator such as the gaussianGradientMagnitude()
421 or the trace of the \ref boundaryTensor(), and the destination \a labels is a label array
422 designating membership of each point in one of the regions found. Plateaus in the boundary
423 indicator are handled via simple tie breaking strategies. Argument \a neighborhood
424 specifies the connectivity between points and can be <tt>DirectNeighborhood</tt> (meaning
425 4-neighborhood in 2D and 6-neighborhood in 3D, default) or <tt>IndirectNeighborhood</tt>
426 (meaning 8-neighborhood in 2D and 26-neighborhood in 3D).
427
428 The watershed variant to be applied can be selected in the \ref WatershedOptions
429 object: When you call <tt>WatershedOptions::regionGrowing()</tt> (default), the flooding
430 algorithm from [1] is used. Alternatively, <tt>WatershedOptions::unionFind()</tt> uses
431 the scan-line algorithm 4.7 from [2]. The latter is faster, but does not support any options
432 (if you pass options nonetheless, they are silently ignored).
433
434 The region growing algorithm needs a seed for each region. Seeds can either be provided in
435 the destination array \a labels (which will then be overwritten with the result) or computed
436 automatically by an internal call to generateWatershedSeeds(). In the former case you have
437 full control over seed placement, while the latter is more convenient. Automatic seed
438 computation is performed when you provide seeding options via <tt>WatershedOptions::seedOptions()</tt>
439 or when the array \a labels is empty (all zeros), in which case default seeding options
440 are chosen. The destination image should be zero-initialized for automatic seed computation.
441
442 Further options to be specified via \ref WatershedOptions are:
443
444 <ul>
445 <li> <tt>keepContours()</tt>: Whether to keep a 1-pixel-wide contour (with label 0) between
446 regions (otherwise, a complete grow is performed, i.e. all pixels are assigned to a region).
447 <li> <tt>stopAtThreshold()</tt>: Whether to stop growing when the boundaryness exceeds a threshold
448 (remaining pixels keep label 0).
449 <li> <tt>biasLabel()</tt>: Whether one region (label) is to be preferred or discouraged by biasing its cost
450 with a given factor (smaller than 1 for preference, larger than 1 for discouragement).
451 </ul>
452
453 The option <tt>turboAlgorithm()</tt> is implied by method <tt>regionGrowing()</tt> (this is
454 in contrast to watershedsRegionGrowing(), which supports an additional algorithm in 2D only).
455
456 watershedsMultiArray() returns the number of regions found (= the highest region label, because
457 labels start at 1).
458
459 <b> Declaration:</b>
460
461 \code
462 namespace vigra {
463 template <unsigned int N, class T, class S1,
464 class Label, class S2>
465 Label
466 watershedsMultiArray(MultiArrayView<N, T, S1> const & data,
467 MultiArrayView<N, Label, S2> labels, // may also hold input seeds
468 NeighborhoodType neighborhood = DirectNeighborhood,
469 WatershedOptions const & options = WatershedOptions());
470 }
471 \endcode
472
473 <b> Usage:</b>
474
475 <b>\#include</b> <vigra/multi_watersheds.hxx><br>
476 Namespace: vigra
477
478 Example: watersheds of the gradient magnitude (the example works likewise for higher dimensions).
479
480 \code
481 MultiArray<2, unsigned char> src(Shape2(w, h));
482 ... // read input data
483
484 // compute gradient magnitude at scale 1.0 as a boundary indicator
485 MultiArray<2, float> gradMag(src.shape());
486 gaussianGradientMagnitude(srcImageRange(src), destImage(gradMag), 1.0);
487
488 // example 1
489 {
490 // the pixel type of the destination image must be large enough to hold
491 // numbers up to 'max_region_label' to prevent overflow
492 MultiArray<2, unsigned int> labeling(src.shape());
493
494 // call region-growing algorithm for 4-neighborhood, leave a 1-pixel boundary between
495 // regions, and autogenerate seeds from all gradient minima where the magnitude is
496 // less than 2.0.
497 unsigned int max_region_label =
498 watershedsMultiArray(gradMag, labeling, DirectNeighborhood,
499 WatershedOptions().keepContours()
500 .seedOptions(SeedOptions().minima().threshold(2.0)));
501 }
502
503 // example 2
504 {
505 MultiArray<2, unsigned int> labeling(src.shape());
506
507 // compute seeds beforehand (use connected components of all pixels
508 // where the gradient is below 4.0)
509 unsigned int max_region_label = generateWatershedSeeds(gradMag, labeling,
510 SeedOptions().levelSets(4.0));
511
512 // quantize the gradient image to 256 gray levels
513 float m, M;
514 gradMag.minmax(&m, &M);
515
516 using namespace multi_math;
517 MultiArray<2, unsigned char> gradMag256(255.0 / (M - m) * (gradMag - m));
518
519 // call region-growing algorithm with 8-neighborhood,
520 // since the data are 8-bit, a faster priority queue will be used
521 watershedsMultiArray(gradMag256, labeling, IndirectNeighborhood);
522 }
523
524 // example 3
525 {
526 MultiArray<2, unsigned int> labeling(src.shape());
527
528 .. // put seeds in 'labeling', e.g. from an interactive labeling program,
529 // make sure that label 1 corresponds to the background
530
531 // bias the watershed algorithm so that the background is preferred
532 // by reducing the cost for label 1 to 90%
533 watershedsMultiArray(gradMag, labeling,
534 WatershedOptions().biasLabel(1, 0.9));
535 }
536
537 // example 4
538 {
539 MultiArray<2, unsigned int> labeling(src.shape());
540
541 // use the fast union-find algorithm with 4-neighborhood
542 watershedsMultiArray(gradMag, labeling, WatershedOptions().unionFind());
543 }
544 \endcode
545*/
546doxygen_overloaded_function(template <...> Label watershedsMultiArray)
547
548 template <unsigned int N, class T, class S1,
549 class Label, class S2>
550 inline Label
551 watershedsMultiArray(MultiArrayView<N, T, S1> const & data,
552 MultiArrayView<N, Label, S2> labels, // may also hold input seeds
553 NeighborhoodType neighborhood = DirectNeighborhood,
554 WatershedOptions const & options = WatershedOptions())
555{
556 vigra_precondition(data.shape() == labels.shape(),
557 "watershedsMultiArray(): Shape mismatch between input and output.");
558
559 GridGraph<N, undirected_tag> graph(data.shape(), neighborhood);
560 return lemon_graph::watershedsGraph(graph, data, labels, options);
561}
562
563//@}
564
565} // namespace vigra
566
567#endif // VIGRA_MULTI_WATERSHEDS_HXX
vigra::GridGraph
Define a grid graph in arbitrary dimensions.
Definition multi_gridgraph.hxx:1429
vigra::MultiArrayView
Base class for, and view to, MultiArray.
Definition multi_array.hxx:705
vigra::MultiArrayView::shape
const difference_type & shape() const
Definition multi_array.hxx:1650
vigra::SeedOptions
Options object for generateWatershedSeeds().
Definition watersheds.hxx:330
vigra::WatershedOptions
Options object for watershed algorithms.
Definition watersheds.hxx:775
vigra
vigra::UInt16
detail::SelectIntegerType< 16, detail::UnsignedIntTypes >::type UInt16
16-bit unsigned int
Definition sized_int.hxx:181
vigra::NeighborhoodType
NeighborhoodType
Choose the neighborhood system in a dimension-independent way.
Definition multi_fwd.hxx:186
vigra::IndirectNeighborhood
@ IndirectNeighborhood
use direct and indirect neighbors
Definition multi_fwd.hxx:188
vigra::DirectNeighborhood
@ DirectNeighborhood
use only direct neighbors
Definition multi_fwd.hxx:187
vigra::watershedsMultiArray
Label watershedsMultiArray(...)
Watershed segmentation of an arbitrary-dimensional array.

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.12.4