1 \section{Structural Analysis and Shape Descriptors}
5 \cvCPyFunc{ApproxChains}
6 Approximates Freeman chain(s) with a polygonal curve.
9 CvSeq* cvApproxChains( \par CvSeq* src\_seq,\par CvMemStorage* storage,\par int method=CV\_CHAIN\_APPROX\_SIMPLE,\par double parameter=0,\par int minimal\_perimeter=0,\par int recursive=0 );
11 \cvdefPy{ApproxChains(src\_seq,storage,method=CV\_CHAIN\_APPROX\_SIMPLE,parameter=0,minimal\_perimeter=0,recursive=0)-> chains}
14 \cvarg{src\_seq}{Pointer to the chain that can refer to other chains}
15 \cvarg{storage}{Storage location for the resulting polylines}
16 \cvarg{method}{Approximation method (see the description of the function \cvCPyCross{FindContours})}
17 \cvarg{parameter}{Method parameter (not used now)}
18 \cvarg{minimal\_perimeter}{Approximates only those contours whose perimeters are not less than \texttt{minimal\_perimeter}. Other chains are removed from the resulting structure}
19 \cvarg{recursive}{If not 0, the function approximates all chains that access can be obtained to from \texttt{src\_seq} by using the \texttt{h\_next} or \texttt{v\_next links}. If 0, the single chain is approximated}
22 This is a stand-alone approximation routine. The function \texttt{cvApproxChains} works exactly in the same way as \cvCPyCross{FindContours} with the corresponding approximation flag. The function returns pointer to the first resultant contour. Other approximated contours, if any, can be accessed via the \texttt{v\_next} or \texttt{h\_next} fields of the returned structure.
24 \cvCPyFunc{ApproxPoly}
25 Approximates polygonal curve(s) with the specified precision.
28 CvSeq* cvApproxPoly( \par const void* src\_seq,\par int header\_size,\par CvMemStorage* storage,\par int method,\par double parameter,\par int parameter2=0 );
31 ApproxPoly(src\_seq, storage, method, parameter=0, parameter2=0) -> sequence
35 \cvarg{src\_seq}{Sequence of an array of points}
37 \cvarg{header\_size}{Header size of the approximated curve[s]}
39 \cvarg{storage}{Container for the approximated contours. If it is NULL, the input sequences' storage is used}
40 \cvarg{method}{Approximation method; only \texttt{CV\_POLY\_APPROX\_DP} is supported, that corresponds to the Douglas-Peucker algorithm}
41 \cvarg{parameter}{Method-specific parameter; in the case of \texttt{CV\_POLY\_APPROX\_DP} it is a desired approximation accuracy}
42 \cvarg{parameter2}{If case if \texttt{src\_seq} is a sequence, the parameter determines whether the single sequence should be approximated or all sequences on the same level or below \texttt{src\_seq} (see \cvCPyCross{FindContours} for description of hierarchical contour structures). If \texttt{src\_seq} is an array CvMat* of points, the parameter specifies whether the curve is closed (\texttt{parameter2}!=0) or not (\texttt{parameter2} =0)}
45 The function approximates one or more curves and
46 returns the approximation result[s]. In the case of multiple curves,
47 the resultant tree will have the same structure as the input one (1:1
51 Calculates the contour perimeter or the curve length.
54 double cvArcLength( \par const void* curve,\par CvSlice slice=CV\_WHOLE\_SEQ,\par int isClosed=-1 );
56 \cvdefPy{ArcLength(curve,slice=CV\_WHOLE\_SEQ,isClosed=-1)-> double}
59 \cvarg{curve}{Sequence or array of the curve points}
60 \cvarg{slice}{Starting and ending points of the curve, by default, the whole curve length is calculated}
61 \cvarg{isClosed}{Indicates whether the curve is closed or not. There are 3 cases:
63 \item $\texttt{isClosed}=0$ the curve is assumed to be unclosed.
64 \item $\texttt{isClosed}>0$ the curve is assumed to be closed.
65 \item $\texttt{isClosed}<0$ if curve is sequence, the flag \texttt{CV\_SEQ\_FLAG\_CLOSED} of \texttt{((CvSeq*)curve)->flags} is checked to determine if the curve is closed or not, otherwise (curve is represented by array (CvMat*) of points) it is assumed to be unclosed.
69 The function calculates the length or curve as the sum of lengths of segments between subsequent points
71 \cvCPyFunc{BoundingRect}
72 Calculates the up-right bounding rectangle of a point set.
75 CvRect cvBoundingRect( CvArr* points, int update=0 );
76 }\cvdefPy{BoundingRect(points,update=0)-> CvRect}
79 \cvarg{points}{2D point set, either a sequence or vector (\texttt{CvMat}) of points}
80 \cvarg{update}{The update flag. See below.}
83 The function returns the up-right bounding rectangle for a 2d point set.
84 Here is the list of possible combination of the flag values and type of \texttt{points}:
86 \begin{tabular}{|c|c|p{3in}|}
88 update & points & action \\ \hline
89 0 & \texttt{CvContour\*} & the bounding rectangle is not calculated, but it is taken from \texttt{rect} field of the contour header.\\ \hline
90 1 & \texttt{CvContour\*} & the bounding rectangle is calculated and written to \texttt{rect} field of the contour header.\\ \hline
91 0 & \texttt{CvSeq\*} or \texttt{CvMat\*} & the bounding rectangle is calculated and returned.\\ \hline
92 1 & \texttt{CvSeq\*} or \texttt{CvMat\*} & runtime error is raised.\\ \hline
96 Finds the box vertices.
99 void cvBoxPoints( \par CvBox2D box,\par CvPoint2D32f pt[4] );
100 }\cvdefPy{BoxPoints(box)-> points}
104 \cvarg{points}{Array of vertices}
107 The function calculates the vertices of the input 2d box.
110 Here is the function code:
113 void cvBoxPoints( CvBox2D box, CvPoint2D32f pt[4] )
115 float a = (float)cos(box.angle)*0.5f;
116 float b = (float)sin(box.angle)*0.5f;
118 pt[0].x = box.center.x - a*box.size.height - b*box.size.width;
119 pt[0].y = box.center.y + b*box.size.height - a*box.size.width;
120 pt[1].x = box.center.x + a*box.size.height - b*box.size.width;
121 pt[1].y = box.center.y - b*box.size.height - a*box.size.width;
122 pt[2].x = 2*box.center.x - pt[0].x;
123 pt[2].y = 2*box.center.y - pt[0].y;
124 pt[3].x = 2*box.center.x - pt[1].x;
125 pt[3].y = 2*box.center.y - pt[1].y;
131 Calculates a pair-wise geometrical histogram for a contour.
134 void cvCalcPGH( const CvSeq* contour, CvHistogram* hist );
135 }\cvdefPy{CalcPGH(contour,hist)-> None}
138 \cvarg{contour}{Input contour. Currently, only integer point coordinates are allowed}
139 \cvarg{hist}{Calculated histogram; must be two-dimensional}
142 The function calculates a
143 2D pair-wise geometrical histogram (PGH), described in
144 \cvCPyCross{Iivarinen97}
145 for the contour. The algorithm considers every pair of contour
146 edges. The angle between the edges and the minimum/maximum distances
147 are determined for every pair. To do this each of the edges in turn
148 is taken as the base, while the function loops through all the other
149 edges. When the base edge and any other edge are considered, the minimum
150 and maximum distances from the points on the non-base edge and line of
151 the base edge are selected. The angle between the edges defines the row
152 of the histogram in which all the bins that correspond to the distance
153 between the calculated minimum and maximum distances are incremented
154 (that is, the histogram is transposed relatively to the \cvCPyCross{Iivarninen97}
155 definition). The histogram can be used for contour matching.
158 Computes the "minimal work" distance between two weighted point configurations.
161 float cvCalcEMD2( \par const CvArr* signature1,\par const CvArr* signature2,\par int distance\_type,\par CvDistanceFunction distance\_func=NULL,\par const CvArr* cost\_matrix=NULL,\par CvArr* flow=NULL,\par float* lower\_bound=NULL,\par void* userdata=NULL );
162 }\cvdefPy{CalcEMD2(signature1, signature2, distance\_type, distance\_func = None, cost\_matrix=None, flow=None, lower\_bound=None, userdata = None) -> float}
165 \cvarg{signature1}{First signature, a $\texttt{size1}\times \texttt{dims}+1$ floating-point matrix. Each row stores the point weight followed by the point coordinates. The matrix is allowed to have a single column (weights only) if the user-defined cost matrix is used}
166 \cvarg{signature2}{Second signature of the same format as \texttt{signature1}, though the number of rows may be different. The total weights may be different, in this case an extra "dummy" point is added to either \texttt{signature1} or \texttt{signature2}}
167 \cvarg{distance\_type}{Metrics used; \texttt{CV\_DIST\_L1, CV\_DIST\_L2}, and \texttt{CV\_DIST\_C} stand for one of the standard metrics; \texttt{CV\_DIST\_USER} means that a user-defined function \texttt{distance\_func} or pre-calculated \texttt{cost\_matrix} is used}
169 \cvarg{distance\_func}{The user-supplied distance function. It takes coordinates of two points and returns the distance between the points
171 typedef float (*CvDistanceFunction)(const float* f1, const float* f2, void* userdata);
175 \cvarg{distance\_func}{The user-supplied distance function. It takes coordinates of two points \texttt{pt0} and \texttt{pt1}, and returns the distance between the points, with sigature
177 func(pt0, pt1, userdata) -> float
181 \cvarg{cost\_matrix}{The user-defined $\texttt{size1}\times \texttt{size2}$ cost matrix. At least one of \texttt{cost\_matrix} and \texttt{distance\_func} must be NULL. Also, if a cost matrix is used, lower boundary (see below) can not be calculated, because it needs a metric function}
182 \cvarg{flow}{The resultant $\texttt{size1} \times \texttt{size2}$ flow matrix: $\texttt{flow}_{i,j}$ is a flow from $i$ th point of \texttt{signature1} to $j$ th point of \texttt{signature2}}
183 \cvarg{lower\_bound}{Optional input/output parameter: lower boundary of distance between the two signatures that is a distance between mass centers. The lower boundary may not be calculated if the user-defined cost matrix is used, the total weights of point configurations are not equal, or if the signatures consist of weights only (i.e. the signature matrices have a single column). The user \textbf{must} initialize \texttt{*lower\_bound}. If the calculated distance between mass centers is greater or equal to \texttt{*lower\_bound} (it means that the signatures are far enough) the function does not calculate EMD. In any case \texttt{*lower\_bound} is set to the calculated distance between mass centers on return. Thus, if user wants to calculate both distance between mass centers and EMD, \texttt{*lower\_bound} should be set to 0}
184 \cvarg{userdata}{Pointer to optional data that is passed into the user-defined distance function}
187 The function computes the earth mover distance and/or
188 a lower boundary of the distance between the two weighted point
189 configurations. One of the applications described in \cvCPyCross{RubnerSept98} is
190 multi-dimensional histogram comparison for image retrieval. EMD is a a
191 transportation problem that is solved using some modification of a simplex
192 algorithm, thus the complexity is exponential in the worst case, though, on average
193 it is much faster. In the case of a real metric the lower boundary
194 can be calculated even faster (using linear-time algorithm) and it can
195 be used to determine roughly whether the two signatures are far enough
196 so that they cannot relate to the same object.
198 \cvCPyFunc{CheckContourConvexity}
199 Tests contour convexity.
202 int cvCheckContourConvexity( const CvArr* contour );
203 }\cvdefPy{CheckContourConvexity(contour)-> int}
206 \cvarg{contour}{Tested contour (sequence or array of points)}
209 The function tests whether the input contour is convex or not. The contour must be simple, without self-intersections.
211 \cvclass{CvConvexityDefect}\label{CvConvexityDefect}
214 Structure describing a single contour convexity defect.
217 typedef struct CvConvexityDefect
219 CvPoint* start; /* point of the contour where the defect begins */
220 CvPoint* end; /* point of the contour where the defect ends */
221 CvPoint* depth_point; /* the farthest from the convex hull point within the defect */
222 float depth; /* distance between the farthest point and the convex hull */
227 A single contour convexity defect, represented by a tuple \texttt{(start, end, depthpoint, depth)}.
230 \cvarg{start}{(x, y) point of the contour where the defect begins}
231 \cvarg{end}{(x, y) point of the contour where the defect ends}
232 \cvarg{depthpoint}{(x, y) point farthest from the convex hull point within the defect}
233 \cvarg{depth}{distance between the farthest point and the convex hull}
238 % ===== Picture. Convexity defects of hand contour. =====
239 \includegraphics[width=0.5\textwidth]{pics/defects.png}
241 \cvCPyFunc{ContourArea}
242 Calculates the area of a whole contour or a contour section.
245 double cvContourArea( \par const CvArr* contour, \par CvSlice slice=CV\_WHOLE\_SEQ );
247 \cvdefPy{ContourArea(contour,slice=CV\_WHOLE\_SEQ)-> double}
250 \cvarg{contour}{Contour (sequence or array of vertices)}
251 \cvarg{slice}{Starting and ending points of the contour section of interest, by default, the area of the whole contour is calculated}
254 The function calculates the area of a whole contour
255 or a contour section. In the latter case the total area bounded by the
256 contour arc and the chord connecting the 2 selected points is calculated
257 as shown on the picture below:
259 \includegraphics[width=0.5\textwidth]{pics/contoursecarea.png}
261 Orientation of the contour affects the area sign, thus the function may return a \emph{negative} result. Use the \texttt{fabs()} function from C runtime to get the absolute value of the area.
263 \cvCPyFunc{ContourFromContourTree}
264 Restores a contour from the tree.
267 CvSeq* cvContourFromContourTree( \par const CvContourTree* tree,\par CvMemStorage* storage,\par CvTermCriteria criteria );
268 }\cvdefPy{ContourFromContourTree(tree,storage,criteria)-> contour}
271 \cvarg{tree}{Contour tree}
272 \cvarg{storage}{Container for the reconstructed contour}
273 \cvarg{criteria}{Criteria, where to stop reconstruction}
276 The function restores the contour from its binary tree representation. The parameter \texttt{criteria} determines the accuracy and/or the number of tree levels used for reconstruction, so it is possible to build an approximated contour. The function returns the reconstructed contour.
278 \cvCPyFunc{ConvexHull2}
279 Finds the convex hull of a point set.
282 CvSeq* cvConvexHull2( \par const CvArr* input,\par void* storage=NULL,\par int orientation=CV\_CLOCKWISE,\par int return\_points=0 );
284 \cvdefPy{ConvexHull2(points,storage,orientation=CV\_CLOCKWISE,return\_points=0)-> convex\_hull}
287 \cvarg{points}{Sequence or array of 2D points with 32-bit integer or floating-point coordinates}
288 \cvarg{storage}{The destination array (CvMat*) or memory storage (CvMemStorage*) that will store the convex hull. If it is an array, it should be 1d and have the same number of elements as the input array/sequence. On output the header is modified as to truncate the array down to the hull size. If \texttt{storage} is NULL then the convex hull will be stored in the same storage as the input sequence}
289 \cvarg{orientation}{Desired orientation of convex hull: \texttt{CV\_CLOCKWISE} or \texttt{CV\_COUNTER\_CLOCKWISE}}
290 \cvarg{return\_points}{If non-zero, the points themselves will be stored in the hull instead of indices if \texttt{storage} is an array, or pointers if \texttt{storage} is memory storage}
293 The function finds the convex hull of a 2D point set using Sklansky's algorithm. If \texttt{storage} is memory storage, the function creates a sequence containing the hull points or pointers to them, depending on \texttt{return\_points} value and returns the sequence on output. If \texttt{storage} is a CvMat, the function returns NULL.
297 Example. Building convex hull for a sequence or array of points
304 #define ARRAY 0 /* switch between array/sequence method by replacing 0<=>1 */
306 void main( int argc, char** argv )
308 IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 );
309 cvNamedWindow( "hull", 1 );
312 CvMemStorage* storage = cvCreateMemStorage();
317 int i, count = rand()%100 + 1, hullcount;
320 CvSeq* ptseq = cvCreateSeq( CV_SEQ_KIND_GENERIC|CV_32SC2,
326 for( i = 0; i < count; i++ )
328 pt0.x = rand() % (img->width/2) + img->width/4;
329 pt0.y = rand() % (img->height/2) + img->height/4;
330 cvSeqPush( ptseq, &pt0 );
332 hull = cvConvexHull2( ptseq, 0, CV_CLOCKWISE, 0 );
333 hullcount = hull->total;
335 CvPoint* points = (CvPoint*)malloc( count * sizeof(points[0]));
336 int* hull = (int*)malloc( count * sizeof(hull[0]));
337 CvMat point_mat = cvMat( 1, count, CV_32SC2, points );
338 CvMat hull_mat = cvMat( 1, count, CV_32SC1, hull );
340 for( i = 0; i < count; i++ )
342 pt0.x = rand() % (img->width/2) + img->width/4;
343 pt0.y = rand() % (img->height/2) + img->height/4;
346 cvConvexHull2( &point_mat, &hull_mat, CV_CLOCKWISE, 0 );
347 hullcount = hull_mat.cols;
350 for( i = 0; i < count; i++ )
353 pt0 = *CV_GET_SEQ_ELEM( CvPoint, ptseq, i );
357 cvCircle( img, pt0, 2, CV_RGB( 255, 0, 0 ), CV_FILLED );
361 pt0 = **CV_GET_SEQ_ELEM( CvPoint*, hull, hullcount - 1 );
363 pt0 = points[hull[hullcount-1]];
366 for( i = 0; i < hullcount; i++ )
369 CvPoint pt = **CV_GET_SEQ_ELEM( CvPoint*, hull, i );
371 CvPoint pt = points[hull[i]];
373 cvLine( img, pt0, pt, CV_RGB( 0, 255, 0 ));
377 cvShowImage( "hull", img );
379 int key = cvWaitKey(0);
380 if( key == 27 ) // 'ESC'
384 cvClearMemStorage( storage );
394 \cvCPyFunc{ConvexityDefects}
395 Finds the convexity defects of a contour.
398 CvSeq* cvConvexityDefects( \par const CvArr* contour,\par const CvArr* convexhull,\par CvMemStorage* storage=NULL );
399 }\cvdefPy{ConvexityDefects(contour,convexhull,storage)-> convexity\_defects}
402 \cvarg{contour}{Input contour}
403 \cvarg{convexhull}{Convex hull obtained using \cvCPyCross{ConvexHull2} that should contain pointers or indices to the contour points, not the hull points themselves (the \texttt{return\_points} parameter in \cvCPyCross{ConvexHull2} should be 0)}
404 \cvarg{storage}{Container for the output sequence of convexity defects. If it is NULL, the contour or hull (in that order) storage is used}
407 The function finds all convexity defects of the input contour and returns a sequence of the CvConvexityDefect structures.
409 \cvCPyFunc{CreateContourTree}
410 Creates a hierarchical representation of a contour.
413 CvContourTree* cvCreateContourTree( \par const CvSeq* contour,\par CvMemStorage* storage,\par double threshold );
415 \cvdefPy{CreateContourTree(contour,storage,threshold)-> contour\_tree}
418 \cvarg{contour}{Input contour}
419 \cvarg{storage}{Container for output tree}
420 \cvarg{threshold}{Approximation accuracy}
423 The function creates a binary tree representation for the input \texttt{contour} and returns the pointer to its root. If the parameter \texttt{threshold} is less than or equal to 0, the function creates a full binary tree representation. If the threshold is greater than 0, the function creates a representation with the precision \texttt{threshold}: if the vertices with the interceptive area of its base line are less than \texttt{threshold}, the tree should not be built any further. The function returns the created tree.
427 \cvCPyFunc{EndFindContours}
428 Finishes the scanning process.
431 CvSeq* cvEndFindContours( \par CvContourScanner* scanner );
435 \cvarg{scanner}{Pointer to the contour scanner}
438 The function finishes the scanning process and returns a pointer to the first contour on the highest level.
442 \cvCPyFunc{FindContours}
443 Finds the contours in a binary image.
446 int cvFindContours(\par CvArr* image,\par CvMemStorage* storage,\par CvSeq** first\_contour,\par
447 int header\_size=sizeof(CvContour),\par int mode=CV\_RETR\_LIST,\par
448 int method=CV\_CHAIN\_APPROX\_SIMPLE,\par CvPoint offset=cvPoint(0,0) );
450 \cvdefPy{FindContours(image, storage, mode=CV\_RETR\_LIST, method=CV\_CHAIN\_APPROX\_SIMPLE, offset=(0,0)) -> cvseq}
453 \cvarg{image}{The source, an 8-bit single channel image. Non-zero pixels are treated as 1's, zero pixels remain 0's - the image is treated as \texttt{binary}. To get such a binary image from grayscale, one may use \cvCPyCross{Threshold}, \cvCPyCross{AdaptiveThreshold} or \cvCPyCross{Canny}. The function modifies the source image's content}
454 \cvarg{storage}{Container of the retrieved contours}
456 \cvarg{first\_contour}{Output parameter, will contain the pointer to the first outer contour}
457 \cvarg{header\_size}{Size of the sequence header, $\ge \texttt{sizeof(CvChain)}$ if $\texttt{method} =\texttt{CV\_CHAIN\_CODE}$,
458 and $\ge \texttt{sizeof(CvContour)}$ otherwise}
460 \cvarg{mode}{Retrieval mode
462 \cvarg{CV\_RETR\_EXTERNAL}{retrives only the extreme outer contours}
463 \cvarg{CV\_RETR\_LIST}{retrieves all of the contours and puts them in the list}
464 \cvarg{CV\_RETR\_CCOMP}{retrieves all of the contours and organizes them into a two-level hierarchy: on the top level are the external boundaries of the components, on the second level are the boundaries of the holes}
465 \cvarg{CV\_RETR\_TREE}{retrieves all of the contours and reconstructs the full hierarchy of nested contours}
467 \cvarg{method}{Approximation method (for all the modes, except \texttt{CV\_LINK\_RUNS}, which uses built-in approximation)
469 \cvarg{CV\_CHAIN\_CODE}{outputs contours in the Freeman chain code. All other methods output polygons (sequences of vertices)}
470 \cvarg{CV\_CHAIN\_APPROX\_NONE}{translates all of the points from the chain code into points}
471 \cvarg{CV\_CHAIN\_APPROX\_SIMPLE}{compresses horizontal, vertical, and diagonal segments and leaves only their end points}
472 \cvarg{CV\_CHAIN\_APPROX\_TC89\_L1,CV\_CHAIN\_APPROX\_TC89\_KCOS}{applies one of the flavors of the Teh-Chin chain approximation algorithm.}
473 \cvarg{CV\_LINK\_RUNS}{uses a completely different contour retrieval algorithm by linking horizontal segments of 1's. Only the \texttt{CV\_RETR\_LIST} retrieval mode can be used with this method.}
475 \cvarg{offset}{Offset, by which every contour point is shifted. This is useful if the contours are extracted from the image ROI and then they should be analyzed in the whole image context}
478 The function retrieves contours from the
479 binary image and returns the number of retrieved contours. The
480 pointer \texttt{first\_contour} is filled by the function. It will
481 contain a pointer to the first outermost contour or \texttt{NULL} if no
482 contours are detected (if the image is completely black). Other
483 contours may be reached from \texttt{first\_contour} using the
484 \texttt{h\_next} and \texttt{v\_next} links. The sample in the
485 \cvCPyCross{DrawContours} discussion shows how to use contours for
486 connected component detection. Contours can be also used for shape
487 analysis and object recognition - see \texttt{squares.c} in the OpenCV
493 \cvCPyFunc{FindNextContour}
494 Finds the next contour in the image.
497 CvSeq* cvFindNextContour( \par CvContourScanner scanner );
501 \cvarg{scanner}{Contour scanner initialized by \cvCPyCross{StartFindContours} }
504 The function locates and retrieves the next contour in the image and returns a pointer to it. The function returns NULL if there are no more contours.
508 \cvCPyFunc{FitEllipse2}
509 Fits an ellipse around a set of 2D points.
512 CvBox2D cvFitEllipse2( \par const CvArr* points );
514 \cvdefPy{FitEllipse2(points)-> Box2D}
517 \cvarg{points}{Sequence or array of points}
520 The function calculates the ellipse that fits best
521 (in least-squares sense) around a set of 2D points. The meaning of the
522 returned structure fields is similar to those in \cvCPyCross{Ellipse} except
523 that \texttt{size} stores the full lengths of the ellipse axises,
527 Fits a line to a 2D or 3D point set.
530 void cvFitLine( \par const CvArr* points,\par int dist\_type,\par double param,\par double reps,\par double aeps,\par float* line );
532 \cvdefPy{FitLine(points, dist\_type, param, reps, aeps) -> line}
535 \cvarg{points}{Sequence or array of 2D or 3D points with 32-bit integer or floating-point coordinates}
536 \cvarg{dist\_type}{The distance used for fitting (see the discussion)}
537 \cvarg{param}{Numerical parameter (\texttt{C}) for some types of distances, if 0 then some optimal value is chosen}
538 \cvarg{reps}{Sufficient accuracy for the radius (distance between the coordinate origin and the line). 0.01 is a good default value.}
539 \cvarg{aeps}{Sufficient accuracy for the angle. 0.01 is a good default value.}
540 \cvarg{line}{The output line parameters. In the case of a 2d fitting,
541 it is \cvC{an array} \cvPy{a tuple} of 4 floats \texttt{(vx, vy, x0, y0)} where \texttt{(vx, vy)} is a normalized vector collinear to the
542 line and \texttt{(x0, y0)} is some point on the line. in the case of a
543 3D fitting it is \cvC{an array} \cvPy{a tuple} of 6 floats \texttt{(vx, vy, vz, x0, y0, z0)}
544 where \texttt{(vx, vy, vz)} is a normalized vector collinear to the line
545 and \texttt{(x0, y0, z0)} is some point on the line}
548 The function fits a line to a 2D or 3D point set by minimizing $\sum_i \rho(r_i)$ where $r_i$ is the distance between the $i$ th point and the line and $\rho(r)$ is a distance function, one of:
552 \item[dist\_type=CV\_DIST\_L2]
553 \[ \rho(r) = r^2/2 \quad \text{(the simplest and the fastest least-squares method)} \]
555 \item[dist\_type=CV\_DIST\_L1]
558 \item[dist\_type=CV\_DIST\_L12]
559 \[ \rho(r) = 2 \cdot (\sqrt{1 + \frac{r^2}{2}} - 1) \]
561 \item[dist\_type=CV\_DIST\_FAIR]
562 \[ \rho\left(r\right) = C^2 \cdot \left( \frac{r}{C} - \log{\left(1 + \frac{r}{C}\right)}\right) \quad \text{where} \quad C=1.3998 \]
564 \item[dist\_type=CV\_DIST\_WELSCH]
565 \[ \rho\left(r\right) = \frac{C^2}{2} \cdot \left( 1 - \exp{\left(-\left(\frac{r}{C}\right)^2\right)}\right) \quad \text{where} \quad C=2.9846 \]
567 \item[dist\_type=CV\_DIST\_HUBER]
570 {C \cdot (r-C/2)}{otherwise} \quad \text{where} \quad C=1.345
574 \cvCPyFunc{GetCentralMoment}
575 Retrieves the central moment from the moment state structure.
578 double cvGetCentralMoment( \par CvMoments* moments,\par int x\_order,\par int y\_order );
580 \cvdefPy{GetCentralMoment(moments, x\_order, y\_order) -> double}
583 \cvarg{moments}{Pointer to the moment state structure}
584 \cvarg{x\_order}{x order of the retrieved moment, $\texttt{x\_order} >= 0$}
585 \cvarg{y\_order}{y order of the retrieved moment, $\texttt{y\_order} >= 0$ and $\texttt{x\_order} + \texttt{y\_order} <= 3$}
588 The function retrieves the central moment, which in the case of image moments is defined as:
591 \mu_{x\_order, \, y\_order} = \sum_{x,y} (I(x,y) \cdot (x-x_c)^{x\_order} \cdot (y-y_c)^{y\_order})
594 where $x_c,y_c$ are the coordinates of the gravity center:
597 x_c=\frac{M_{10}}{M_{00}}, y_c=\frac{M_{01}}{M_{00}}
600 \cvCPyFunc{GetHuMoments}
601 Calculates the seven Hu invariants.
603 \cvdefC{void cvGetHuMoments( const CvMoments* moments,CvHuMoments* hu );}
604 \cvdefPy{GetHuMoments(moments) -> hu}
607 \cvarg{moments}{The input moments, computed with \cvCPyCross{Moments}}
608 \cvarg{hu}{The output Hu invariants}
611 The function calculates the seven Hu invariants, see \url{http://en.wikipedia.org/wiki/Image_moment}, that are defined as:
614 hu_1=\eta_{20}+\eta_{02}\\
615 hu_2=(\eta_{20}-\eta_{02})^{2}+4\eta_{11}^{2}\\
616 hu_3=(\eta_{30}-3\eta_{12})^{2}+ (3\eta_{21}-\eta_{03})^{2}\\
617 hu_4=(\eta_{30}+\eta_{12})^{2}+ (\eta_{21}+\eta_{03})^{2}\\
618 hu_5=(\eta_{30}-3\eta_{12})(\eta_{30}+\eta_{12})[(\eta_{30}+\eta_{12})^{2}-3(\eta_{21}+\eta_{03})^{2}]+(3\eta_{21}-\eta_{03})(\eta_{21}+\eta_{03})[3(\eta_{30}+\eta_{12})^{2}-(\eta_{21}+\eta_{03})^{2}]\\
619 hu_6=(\eta_{20}-\eta_{02})[(\eta_{30}+\eta_{12})^{2}- (\eta_{21}+\eta_{03})^{2}]+4\eta_{11}(\eta_{30}+\eta_{12})(\eta_{21}+\eta_{03})\\
620 hu_7=(3\eta_{21}-\eta_{03})(\eta_{21}+\eta_{03})[3(\eta_{30}+\eta_{12})^{2}-(\eta_{21}+\eta_{03})^{2}]-(\eta_{30}-3\eta_{12})(\eta_{21}+\eta_{03})[3(\eta_{30}+\eta_{12})^{2}-(\eta_{21}+\eta_{03})^{2}]\\
624 where $\eta_{ji}$ denote the normalized central moments.
626 These values are proved to be invariant to the image scale, rotation, and reflection except the seventh one, whose sign is changed by reflection. Of course, this invariance was proved with the assumption of infinite image resolution. In case of a raster images the computed Hu invariants for the original and transformed images will be a bit different.
631 >>> original = cv.LoadImageM("building.jpg", cv.CV_LOAD_IMAGE_GRAYSCALE)
632 >>> print cv.GetHuMoments(cv.Moments(original))
633 (0.0010620951868446141, 1.7962726159653835e-07, 1.4932744974469421e-11, 4.4832441315737963e-12, -1.0819359198251739e-23, -9.5726503811945833e-16, -3.5050592804744648e-23)
634 >>> flipped = cv.CloneMat(original)
635 >>> cv.Flip(original, flipped)
636 >>> print cv.GetHuMoments(cv.Moments(flipped))
637 (0.0010620951868446141, 1.796272615965384e-07, 1.4932744974469935e-11, 4.4832441315740249e-12, -1.0819359198259393e-23, -9.572650381193327e-16, 3.5050592804745877e-23)
641 \cvCPyFunc{GetNormalizedCentralMoment}
642 Retrieves the normalized central moment from the moment state structure.
645 double cvGetNormalizedCentralMoment( \par CvMoments* moments,\par int x\_order,\par int y\_order );
646 }\cvdefPy{GetNormalizedCentralMoment(moments, x\_order, y\_order) -> double}
649 \cvarg{moments}{Pointer to the moment state structure}
650 \cvarg{x\_order}{x order of the retrieved moment, $\texttt{x\_order} >= 0$}
651 \cvarg{y\_order}{y order of the retrieved moment, $\texttt{y\_order} >= 0$ and $\texttt{x\_order} + \texttt{y\_order} <= 3$}
654 The function retrieves the normalized central moment:
657 \eta_{x\_order, \, y\_order} = \frac{\mu_{x\_order, \, y\_order}}{M_{00}^{(y\_order+x\_order)/2+1}}
660 \cvCPyFunc{GetSpatialMoment}
661 Retrieves the spatial moment from the moment state structure.
664 double cvGetSpatialMoment( \par CvMoments* moments, \par int x\_order, \par int y\_order );
666 \cvdefPy{GetSpatialMoment(moments, x\_order, y\_order) -> double}
669 \cvarg{moments}{The moment state, calculated by \cvCPyCross{Moments}}
670 \cvarg{x\_order}{x order of the retrieved moment, $\texttt{x\_order} >= 0$}
671 \cvarg{y\_order}{y order of the retrieved moment, $\texttt{y\_order} >= 0$ and $\texttt{x\_order} + \texttt{y\_order} <= 3$}
674 The function retrieves the spatial moment, which in the case of image moments is defined as:
677 M_{x\_order, \, y\_order} = \sum_{x,y} (I(x,y) \cdot x^{x\_order} \cdot y^{y\_order})
680 where $I(x,y)$ is the intensity of the pixel $(x, y)$.
682 \cvCPyFunc{MatchContourTrees}
683 Compares two contours using their tree representations.
686 double cvMatchContourTrees( \par const CvContourTree* tree1,\par const CvContourTree* tree2,\par int method,\par double threshold );
687 }\cvdefPy{MatchContourTrees(tree1,tree2,method,threshold)-> double}
690 \cvarg{tree1}{First contour tree}
691 \cvarg{tree2}{Second contour tree}
692 \cvarg{method}{Similarity measure, only \texttt{CV\_CONTOUR\_TREES\_MATCH\_I1} is supported}
693 \cvarg{threshold}{Similarity threshold}
696 The function calculates the value of the matching measure for two contour trees. The similarity measure is calculated level by level from the binary tree roots. If at a certain level the difference between contours becomes less than \texttt{threshold}, the reconstruction process is interrupted and the current difference is returned.
698 \cvCPyFunc{MatchShapes}
702 double cvMatchShapes( \par const void* object1,\par const void* object2,\par int method,\par double parameter=0 );
703 }\cvdefPy{MatchShapes(object1,object2,method,parameter=0)-> None}
706 \cvarg{object1}{First contour or grayscale image}
707 \cvarg{object2}{Second contour or grayscale image}
708 \cvarg{method}{Comparison method;
709 \texttt{CV\_CONTOUR\_MATCH\_I1},
710 \texttt{CV\_CONTOURS\_MATCH\_I2}
712 \texttt{CV\_CONTOURS\_MATCH\_I3}}
713 \cvarg{parameter}{Method-specific parameter (is not used now)}
716 The function compares two shapes. The 3 implemented methods all use Hu moments (see \cvCPyCross{GetHuMoments}) ($A$ is \texttt{object1}, $B$ is \texttt{object2}):
719 \item[method=CV\_CONTOUR\_MATCH\_I1]
720 \[ I_1(A,B) = \sum_{i=1...7} \left| \frac{1}{m^A_i} - \frac{1}{m^B_i} \right| \]
722 \item[method=CV\_CONTOUR\_MATCH\_I2]
723 \[ I_2(A,B) = \sum_{i=1...7} \left| m^A_i - m^B_i \right| \]
725 \item[method=CV\_CONTOUR\_MATCH\_I3]
726 \[ I_3(A,B) = \sum_{i=1...7} \frac{ \left| m^A_i - m^B_i \right| }{ \left| m^A_i \right| } \]
733 m^A_i = sign(h^A_i) \cdot \log{h^A_i}
734 m^B_i = sign(h^B_i) \cdot \log{h^B_i}
738 and $h^A_i, h^B_i$ are the Hu moments of $A$ and $B$ respectively.
741 \cvCPyFunc{MinAreaRect2}
742 Finds the circumscribed rectangle of minimal area for a given 2D point set.
745 CvBox2D cvMinAreaRect2( \par const CvArr* points,\par CvMemStorage* storage=NULL );
746 }\cvdefPy{MinAreaRect2(points,storage=NULL)-> CvBox2D}
749 \cvarg{points}{Sequence or array of points}
750 \cvarg{storage}{Optional temporary memory storage}
753 The function finds a circumscribed rectangle of the minimal area for a 2D point set by building a convex hull for the set and applying the rotating calipers technique to the hull.
755 Picture. Minimal-area bounding rectangle for contour
757 \includegraphics[width=0.5\textwidth]{pics/minareabox.png}
759 \cvCPyFunc{MinEnclosingCircle}
760 Finds the circumscribed circle of minimal area for a given 2D point set.
763 int cvMinEnclosingCircle( \par const CvArr* points,\par CvPoint2D32f* center,\par float* radius );
765 \cvdefPy{MinEnclosingCircle(points)-> (int,center,radius)}
768 \cvarg{points}{Sequence or array of 2D points}
769 \cvarg{center}{Output parameter; the center of the enclosing circle}
770 \cvarg{radius}{Output parameter; the radius of the enclosing circle}
773 The function finds the minimal circumscribed
774 circle for a 2D point set using an iterative algorithm. It returns nonzero
775 if the resultant circle contains all the input points and zero otherwise
776 (i.e. the algorithm failed).
779 Calculates all of the moments up to the third order of a polygon or rasterized shape.
782 void cvMoments( \par const CvArr* arr,\par CvMoments* moments,\par int binary=0 );
784 \cvdefPy{Moments(arr, binary = 0) -> moments}
787 \cvarg{arr}{Image (1-channel or 3-channel with COI set) or polygon (CvSeq of points or a vector of points)}
788 \cvarg{moments}{Pointer to returned moment's state structure}
789 \cvarg{binary}{(For images only) If the flag is non-zero, all of the zero pixel values are treated as zeroes, and all of the others are treated as 1's}
792 The function calculates spatial and central moments up to the third order and writes them to \texttt{moments}. The moments may then be used then to calculate the gravity center of the shape, its area, main axises and various shape characeteristics including 7 Hu invariants.
794 \cvCPyFunc{PointPolygonTest}
795 Point in contour test.
798 double cvPointPolygonTest( \par const CvArr* contour,\par CvPoint2D32f pt,\par int measure\_dist );
799 }\cvdefPy{PointPolygonTest(contour,pt,measure\_dist)-> double}
802 \cvarg{contour}{Input contour}
803 \cvarg{pt}{The point tested against the contour}
804 \cvarg{measure\_dist}{If it is non-zero, the function estimates the distance from the point to the nearest contour edge}
807 The function determines whether the
808 point is inside a contour, outside, or lies on an edge (or coinsides
809 with a vertex). It returns positive, negative or zero value,
810 correspondingly. When $\texttt{measure\_dist} =0$, the return value
811 is +1, -1 and 0, respectively. When $\texttt{measure\_dist} \ne 0$,
812 it is a signed distance between the point and the nearest contour
815 Here is the sample output of the function, where each image pixel is tested against the contour.
817 \includegraphics[width=0.5\textwidth]{pics/pointpolygon.png}
821 \cvCPyFunc{PointSeqFromMat}
822 Initializes a point sequence header from a point vector.
825 CvSeq* cvPointSeqFromMat( \par int seq\_kind,\par const CvArr* mat,\par CvContour* contour\_header,\par CvSeqBlock* block );
829 \cvarg{seq\_kind}{Type of the point sequence: point set (0), a curve (\texttt{CV\_SEQ\_KIND\_CURVE}), closed curve (\texttt{CV\_SEQ\_KIND\_CURVE+CV\_SEQ\_FLAG\_CLOSED}) etc.}
830 \cvarg{mat}{Input matrix. It should be a continuous, 1-dimensional vector of points, that is, it should have type \texttt{CV\_32SC2} or \texttt{CV\_32FC2}}
831 \cvarg{contour\_header}{Contour header, initialized by the function}
832 \cvarg{block}{Sequence block header, initialized by the function}
835 The function initializes a sequence
836 header to create a "virtual" sequence in which elements reside in
837 the specified matrix. No data is copied. The initialized sequence
838 header may be passed to any function that takes a point sequence
839 on input. No extra elements can be added to the sequence,
840 but some may be removed. The function is a specialized variant of
841 \cvCPyCross{MakeSeqHeaderForArray} and uses
842 the latter internally. It returns a pointer to the initialized contour
843 header. Note that the bounding rectangle (field \texttt{rect} of
844 \texttt{CvContour} strucuture) is not initialized by the function. If
845 you need one, use \cvCPyCross{BoundingRect}.
847 Here is a simple usage example.
852 CvMat* vector = cvCreateMat( 1, 3, CV_32SC2 );
854 CV_MAT_ELEM( *vector, CvPoint, 0, 0 ) = cvPoint(100,100);
855 CV_MAT_ELEM( *vector, CvPoint, 0, 1 ) = cvPoint(100,200);
856 CV_MAT_ELEM( *vector, CvPoint, 0, 2 ) = cvPoint(200,100);
858 IplImage* img = cvCreateImage( cvSize(300,300), 8, 3 );
862 cvPointSeqFromMat(CV_SEQ_KIND_CURVE+CV_SEQ_FLAG_CLOSED,
868 0, 3, 8, cvPoint(0,0));
872 \cvCPyFunc{ReadChainPoint}
873 Gets the next chain point.
876 CvPoint cvReadChainPoint( CvChainPtReader* reader );
880 \cvarg{reader}{Chain reader state}
883 The function returns the current chain point and updates the reader position.
885 \cvCPyFunc{StartFindContours}
886 Initializes the contour scanning process.
889 CvContourScanner cvStartFindContours(\par CvArr* image,\par CvMemStorage* storage,\par
890 int header\_size=sizeof(CvContour),\par
891 int mode=CV\_RETR\_LIST,\par
892 int method=CV\_CHAIN\_APPROX\_SIMPLE,\par
893 CvPoint offset=cvPoint(0,\par0) );
897 \cvarg{image}{The 8-bit, single channel, binary source image}
898 \cvarg{storage}{Container of the retrieved contours}
899 \cvarg{header\_size}{Size of the sequence header, $>=sizeof(CvChain)$ if \texttt{method} =CV\_CHAIN\_CODE, and $>=sizeof(CvContour)$ otherwise}
900 \cvarg{mode}{Retrieval mode; see \cvCPyCross{FindContours}}
901 \cvarg{method}{Approximation method. It has the same meaning in \cvCPyCross{FindContours}, but \texttt{CV\_LINK\_RUNS} can not be used here}
902 \cvarg{offset}{ROI offset; see \cvCPyCross{FindContours}}
905 The function initializes and returns a pointer to the contour scanner. The scanner is used in \cvCPyCross{FindNextContour} to retrieve the rest of the contours.
907 \cvCPyFunc{StartReadChainPoints}
908 Initializes the chain reader.
911 void cvStartReadChainPoints( CvChain* chain, CvChainPtReader* reader );
914 The function initializes a special reader.
916 \cvCPyFunc{SubstituteContour}
917 Replaces a retrieved contour.
920 void cvSubstituteContour( \par CvContourScanner scanner, \par CvSeq* new\_contour );
924 \cvarg{scanner}{Contour scanner initialized by \cvCPyCross{StartFindContours} }
925 \cvarg{new\_contour}{Substituting contour}
928 The function replaces the retrieved
929 contour, that was returned from the preceding call of
930 \cvCPyCross{FindNextContour} and stored inside the contour scanner
931 state, with the user-specified contour. The contour is inserted
932 into the resulting structure, list, two-level hierarchy, or tree,
933 depending on the retrieval mode. If the parameter \texttt{new\_contour}
934 is \texttt{NULL}, the retrieved contour is not included in the
935 resulting structure, nor are any of its children that might be added
936 to this structure later.
946 Calculates all of the moments up to the third order of a polygon or rasterized shape.
948 \cvdefCpp{Moments moments( const Mat\& array, bool binaryImage=false );}
950 where the class \texttt{Moments} is defined as:
956 Moments(double m00, double m10, double m01, double m20, double m11,
957 double m02, double m30, double m21, double m12, double m03 );
958 Moments( const CvMoments\& moments );
959 operator CvMoments() const;
962 double m00, m10, m01, m20, m11, m02, m30, m21, m12, m03;
964 double mu20, mu11, mu02, mu30, mu21, mu12, mu03;
965 // central normalized moments
966 double nu20, nu11, nu02, nu30, nu21, nu12, nu03;
971 \cvarg{array}{A raster image (single-channel, 8-bit or floating-point 2D array) or an array
972 ($1 \times N$ or $N \times 1$) of 2D points (\texttt{Point} or \texttt{Point2f})}
973 \cvarg{binaryImage}{(For images only) If it is true, then all the non-zero image pixels are treated as 1's}
976 The function computes moments, up to the 3rd order, of a vector shape or a rasterized shape.
977 In case of a raster image, the spatial moments $\texttt{Moments::m}_{ji}$ are computed as:
979 \[\texttt{m}_{ji}=\sum_{x,y} \left(\texttt{array}(x,y) \cdot x^j \cdot y^i\right),\]
981 the central moments $\texttt{Moments::mu}_{ji}$ are computed as:
982 \[\texttt{mu}_{ji}=\sum_{x,y} \left(\texttt{array}(x,y) \cdot (x - \bar{x})^j \cdot (y - \bar{y})^i\right)\]
983 where $(\bar{x}, \bar{y})$ is the mass center:
986 \bar{x}=\frac{\texttt{m}_{10}}{\texttt{m}_{00}},\; \bar{y}=\frac{\texttt{m}_{01}}{\texttt{m}_{00}}
989 and the normalized central moments $\texttt{Moments::nu}_{ij}$ are computed as:
990 \[\texttt{nu}_{ji}=\frac{\texttt{mu}_{ji}}{\texttt{m}_{00}^{(i+j)/2+1}}.\]
992 Note that $\texttt{mu}_{00}=\texttt{m}_{00}$, $\texttt{nu}_{00}=1$ $\texttt{nu}_{10}=\texttt{mu}_{10}=\texttt{mu}_{01}=\texttt{mu}_{10}=0$, hence the values are not stored.
994 The moments of a contour are defined in the same way, but computed using Green's formula
995 (see \url{http://en.wikipedia.org/wiki/Green_theorem}), therefore, because of a limited raster resolution, the moments computed for a contour will be slightly different from the moments computed for the same contour rasterized.
997 See also: \cvCppCross{contourArea}, \cvCppCross{arcLength}
999 \cvCppFunc{HuMoments}
1000 Calculates the seven Hu invariants.
1002 \cvdefCpp{void HuMoments( const Moments\& moments, double h[7] );}
1004 \cvarg{moments}{The input moments, computed with \cvCppCross{moments}}
1005 \cvarg{h}{The output Hu invariants}
1008 The function calculates the seven Hu invariants, see \url{http://en.wikipedia.org/wiki/Image_moment}, that are defined as:
1011 h[0]=\eta_{20}+\eta_{02}\\
1012 h[1]=(\eta_{20}-\eta_{02})^{2}+4\eta_{11}^{2}\\
1013 h[2]=(\eta_{30}-3\eta_{12})^{2}+ (3\eta_{21}-\eta_{03})^{2}\\
1014 h[3]=(\eta_{30}+\eta_{12})^{2}+ (\eta_{21}+\eta_{03})^{2}\\
1015 h[4]=(\eta_{30}-3\eta_{12})(\eta_{30}+\eta_{12})[(\eta_{30}+\eta_{12})^{2}-3(\eta_{21}+\eta_{03})^{2}]+(3\eta_{21}-\eta_{03})(\eta_{21}+\eta_{03})[3(\eta_{30}+\eta_{12})^{2}-(\eta_{21}+\eta_{03})^{2}]\\
1016 h[5]=(\eta_{20}-\eta_{02})[(\eta_{30}+\eta_{12})^{2}- (\eta_{21}+\eta_{03})^{2}]+4\eta_{11}(\eta_{30}+\eta_{12})(\eta_{21}+\eta_{03})\\
1017 h[6]=(3\eta_{21}-\eta_{03})(\eta_{21}+\eta_{03})[3(\eta_{30}+\eta_{12})^{2}-(\eta_{21}+\eta_{03})^{2}]-(\eta_{30}-3\eta_{12})(\eta_{21}+\eta_{03})[3(\eta_{30}+\eta_{12})^{2}-(\eta_{21}+\eta_{03})^{2}]\\
1021 where $\eta_{ji}$ stand for $\texttt{Moments::nu}_{ji}$.
1023 These values are proved to be invariant to the image scale, rotation, and reflection except the seventh one, whose sign is changed by reflection. Of course, this invariance was proved with the assumption of infinite image resolution. In case of a raster images the computed Hu invariants for the original and transformed images will be a bit different.
1025 See also: \cvCppCross{matchShapes}
1027 \cvCppFunc{findContours}
1028 Finds the contours in a binary image.
1030 \cvdefCpp{void findContours( const Mat\& image, vector<vector<Point> >\& contours,\par
1031 vector<Vec4i>\& hierarchy, int mode,\par
1032 int method, Point offset=Point());\newline
1033 void findContours( const Mat\& image, vector<vector<Point> >\& contours,\par
1034 int mode, int method, Point offset=Point());
1037 \cvarg{image}{The source, an 8-bit single-channel image. Non-zero pixels are treated as 1's, zero pixels remain 0's - the image is treated as \texttt{binary}. You can use \cvCppCross{compare}, \cvCppCross{inRange}, \cvCppCross{threshold}, \cvCppCross{adaptiveThreshold}, \cvCppCross{Canny} etc. to create a binary image out of a grayscale or color one. The function modifies the \texttt{image} while extracting the contours}
1038 \cvarg{contours}{The detected contours. Each contour is stored as a vector of points}
1039 \cvarg{hiararchy}{The optional output vector that will contain information about the image topology. It will have as many elements as the number of contours. For each contour \texttt{contours[i]}, the elements \texttt{hierarchy[i][0]}, \texttt{hiearchy[i][1]}, \texttt{hiearchy[i][2]}, \texttt{hiearchy[i][3]} will be set to 0-based indices in \texttt{contours} of the next and previous contours at the same hierarchical level, the first child contour and the parent contour, respectively. If for some contour \texttt{i} there is no next, previous, parent or nested contours, the corresponding elements of \texttt{hierarchy[i]} will be negative}
1040 \cvarg{mode}{The contour retrieval mode
1042 \cvarg{CV\_RETR\_EXTERNAL}{retrieves only the extreme outer contours; It will set \texttt{hierarchy[i][2]=hierarchy[i][3]=-1} for all the contours}
1043 \cvarg{CV\_RETR\_LIST}{retrieves all of the contours without establishing any hierarchical relationships}
1044 \cvarg{CV\_RETR\_CCOMP}{retrieves all of the contours and organizes them into a two-level hierarchy: on the top level are the external boundaries of the components, on the second level are the boundaries of the holes. If inside a hole of a connected component there is another contour, it will still be put on the top level}
1045 \cvarg{CV\_RETR\_TREE}{retrieves all of the contours and reconstructs the full hierarchy of nested contours. This full hierarchy is built and shown in OpenCV \texttt{contours.c} demo}
1047 \cvarg{method}{The contour approximation method.
1049 \cvarg{CV\_CHAIN\_APPROX\_NONE}{stores absolutely all the contour points. That is, every 2 points of a contour stored with this method are 8-connected neighbors of each other}
1050 \cvarg{CV\_CHAIN\_APPROX\_SIMPLE}{compresses horizontal, vertical, and diagonal segments and leaves only their end points. E.g. an up-right rectangular contour will be encoded with 4 points}
1051 \cvarg{CV\_CHAIN\_APPROX\_TC89\_L1,CV\_CHAIN\_APPROX\_TC89\_KCOS}{applies one of the flavors of the Teh-Chin chain approximation algorithm; see \cite{TehChin89}}
1053 \cvarg{offset}{The optional offset, by which every contour point is shifted. This is useful if the contours are extracted from the image ROI and then they should be analyzed in the whole image context}
1056 The function retrieves contours from the
1057 binary image using the algorithm \cite{Suzuki85}. The contours are a useful tool for shape analysis and object detection and recognition. See \texttt{squares.c} in the OpenCV sample directory.
1059 \cvCppFunc{drawContours}
1060 Draws contours' outlines or filled contours.
1062 \cvdefCpp{void drawContours( Mat\& image, const vector<vector<Point> >\& contours,\par
1063 int contourIdx, const Scalar\& color, int thickness=1,\par
1064 int lineType=8, const vector<Vec4i>\& hierarchy=vector<Vec4i>(),\par
1065 int maxLevel=INT\_MAX, Point offset=Point() );}
1067 \cvarg{image}{The destination image}
1068 \cvarg{contours}{All the input contours. Each contour is stored as a point vector}
1069 \cvarg{contourIdx}{Indicates the contour to draw. If it is negative, all the contours are drawn}
1070 \cvarg{color}{The contours' color}
1071 \cvarg{thickness}{Thickness of lines the contours are drawn with.
1072 If it is negative (e.g. \texttt{thickness=CV\_FILLED}), the contour interiors are
1074 \cvarg{lineType}{The line connectivity; see \cvCppCross{line} description}
1075 \cvarg{hierarchy}{The optional information about hierarchy. It is only needed if you want to draw only some of the contours (see \texttt{maxLevel})}
1076 \cvarg{maxLevel}{Maximal level for drawn contours. If 0, only
1077 the specified contour is drawn. If 1, the function draws the contour(s) and all the nested contours. If 2, the function draws the contours, all the nested contours and all the nested into nested contours etc. This parameter is only taken into account when there is \texttt{hierarchy} available.}
1078 \cvarg{offset}{The optional contour shift parameter. Shift all the drawn contours by the specified $\texttt{offset}=(dx,dy)$}
1081 The function draws contour outlines in the image if $\texttt{thickness} \ge 0$ or fills the area bounded by the contours if $ \texttt{thickness}<0$. Here is the example on how to retrieve connected components from the binary image and label them
1085 #include "highgui.h"
1089 int main( int argc, char** argv )
1092 // the first command line parameter must be file name of binary
1093 // (black-n-white) image
1094 if( argc != 2 || !(src=imread(argv[1], 0)).data)
1097 Mat dst = Mat::zeros(src.rows, src.cols, CV_8UC3);
1100 namedWindow( "Source", 1 );
1101 imshow( "Source", src );
1103 vector<vector<Point> > contours;
1104 vector<Vec4i> hierarchy;
1106 findContours( src, contours, hierarchy,
1107 CV_RETR_CCOMP, CV_CHAIN_APPROX_SIMPLE );
1109 // iterate through all the top-level contours,
1110 // draw each connected component with its own random color
1112 for( ; idx >= 0; idx = hiearchy[idx][0] )
1114 Scalar color( rand()&255, rand()&255, rand()&255 );
1115 drawContours( dst, contours, idx, color, CV_FILLED, 8, hiearchy );
1118 namedWindow( "Components", 1 );
1119 imshow( "Components", dst );
1125 \cvCppFunc{approxPolyDP}
1126 Approximates polygonal curve(s) with the specified precision.
1128 \cvdefCpp{void approxPolyDP( const Mat\& curve,\par
1129 vector<Point>\& approxCurve,\par
1130 double epsilon, bool closed );\newline
1131 void approxPolyDP( const Mat\& curve,\par
1132 vector<Point2f>\& approxCurve,\par
1133 double epsilon, bool closed );}
1135 \cvarg{curve}{The polygon or curve to approximate. Must be $1 \times N$ or $N \times 1$ matrix of type \texttt{CV\_32SC2} or \texttt{CV\_32FC2}. You can also convert \texttt{vector<Point>} or \texttt{vector<Point2f} to the matrix by calling \texttt{Mat(const vector<T>\&)} constructor.}
1136 \cvarg{approxCurve}{The result of the approximation; The type should match the type of the input curve}
1137 \cvarg{epsilon}{Specifies the approximation accuracy. This is the maximum distance between the original curve and its approximation}
1138 \cvarg{closed}{If true, the approximated curve is closed (i.e. its first and last vertices are connected), otherwise it's not}
1141 The functions \texttt{approxPolyDP} approximate a curve or a polygon with another curve/polygon with less vertices, so that the distance between them is less or equal to the specified precision. It used Douglas-Peucker algorithm \url{http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm}
1143 \cvCppFunc{arcLength}
1144 Calculates a contour perimeter or a curve length.
1146 \cvdefCpp{double arcLength( const Mat\& curve, bool closed );}
1148 \cvarg{curve}{The input vector of 2D points, represented by \texttt{CV\_32SC2} or \texttt{CV\_32FC2} matrix, or by \texttt{vector<Point>} or \texttt{vector<Point2f>} converted to a matrix with \texttt{Mat(const vector<T>\&)} constructor}
1149 \cvarg{closed}{Indicates, whether the curve is closed or not}
1152 The function computes the curve length or the closed contour perimeter.
1154 \cvCppFunc{boundingRect}
1155 Calculates the up-right bounding rectangle of a point set.
1157 \cvdefCpp{Rect boundingRect( const Mat\& points );}
1159 \cvarg{points}{The input 2D point set, represented by \texttt{CV\_32SC2} or \texttt{CV\_32FC2} matrix, or by \texttt{vector<Point>} or \texttt{vector<Point2f>} converted to the matrix using \texttt{Mat(const vector<T>\&)} constructor.}
1162 The function calculates and returns the minimal up-right bounding rectangle for the specified point set.
1165 \cvCppFunc{estimateRigidTransform}
1166 Computes optimal affine transformation between two 2D point sets
1168 \cvdefCpp{Mat estimateRigidTransform( const Mat\& srcpt, const Mat\& dstpt,\par
1171 \cvarg{srcpt}{The first input 2D point set}
1172 \cvarg{dst}{The second input 2D point set of the same size and the same type as \texttt{A}}
1173 \cvarg{fullAffine}{If true, the function finds the optimal affine transformation with no any additional resrictions (i.e. there are 6 degrees of freedom); otherwise, the class of transformations to choose from is limited to combinations of translation, rotation and uniform scaling (i.e. there are 5 degrees of freedom)}
1176 The function finds the optimal affine transform $[A|b]$ (a $2 \times 3$ floating-point matrix) that approximates best the transformation from $\texttt{srcpt}_i$ to $\texttt{dstpt}_i$:
1178 \[ [A^*|b^*] = arg \min_{[A|b]} \sum_i \|\texttt{dstpt}_i - A {\texttt{srcpt}_i}^T - b \|^2 \]
1180 where $[A|b]$ can be either arbitrary (when \texttt{fullAffine=true}) or have form
1181 \[\begin{bmatrix}a_{11} & a_{12} & b_1 \\ -a_{12} & a_{11} & b_2 \end{bmatrix}\] when \texttt{fullAffine=false}.
1183 See also: \cvCppCross{getAffineTransform}, \cvCppCross{getPerspectiveTransform}, \cvCppCross{findHomography}
1185 \cvCppFunc{estimateAffine3D}
1186 Computes optimal affine transformation between two 3D point sets
1188 \cvdefCpp{int estimateAffine3D(const Mat\& srcpt, const Mat\& dstpt, Mat\& out,\par
1189 vector<uchar>\& outliers,\par
1190 double ransacThreshold = 3.0,\par
1191 double confidence = 0.99);}
1193 \cvarg{srcpt}{The first input 3D point set}
1194 \cvarg{dstpt}{The second input 3D point set}
1195 \cvarg{out}{The output 3D affine transformation matrix $3 \times 4$}
1196 \cvarg{outliers}{The output vector indicating which points are outliers}
1197 \cvarg{ransacThreshold}{The maximum reprojection error in RANSAC algorithm to consider a point an inlier}
1198 \cvarg{confidence}{The confidence level, between 0 and 1, with which the matrix is estimated}
1201 The function estimates the optimal 3D affine transformation between two 3D point sets using RANSAC algorithm.
1204 \cvCppFunc{contourArea}
1205 Calculates the contour area
1207 \cvdefCpp{double contourArea( const Mat\& contour ); }
1209 \cvarg{contour}{The contour vertices, represented by \texttt{CV\_32SC2} or \texttt{CV\_32FC2} matrix, or by \texttt{vector<Point>} or \texttt{vector<Point2f>} converted to the matrix using \texttt{Mat(const vector<T>\&)} constructor.}
1212 The function computes the contour area. Similarly to \cvCppCross{moments} the area is computed using the Green formula, thus the returned area and the number of non-zero pixels, if you draw the contour using \cvCppCross{drawContours} or \cvCppCross{fillPoly}, can be different.
1213 Here is a short example:
1216 vector<Point> contour;
1217 contour.push_back(Point2f(0, 0));
1218 contour.push_back(Point2f(10, 0));
1219 contour.push_back(Point2f(10, 10));
1220 contour.push_back(Point2f(5, 4));
1222 double area0 = contourArea(contour);
1223 vector<Point> approx;
1224 approxPolyDP(contour, approx, 5, true);
1225 double area1 = contourArea(approx);
1227 cout << "area0 =" << area0 << endl <<
1228 "area1 =" << area1 << endl <<
1229 "approx poly vertices" << approx.size() << endl;
1232 \cvCppFunc{convexHull}
1233 Finds the convex hull of a point set.
1235 \cvdefCpp{void convexHull( const Mat\& points, vector<int>\& hull,\par
1236 bool clockwise=false );\newline
1237 void convexHull( const Mat\& points, vector<Point>\& hull,\par
1238 bool clockwise=false );\newline
1239 void convexHull( const Mat\& points, vector<Point2f>\& hull,\par
1240 bool clockwise=false );}
1242 \cvarg{points}{The input 2D point set, represented by \texttt{CV\_32SC2} or \texttt{CV\_32FC2} matrix, or by \texttt{vector<Point>} or \texttt{vector<Point2f>} converted to the matrix using \texttt{Mat(const vector<T>\&)} constructor.}
1243 \cvarg{hull}{The output convex hull. It is either a vector of points that form the hull, or a vector of 0-based point indices of the hull points in the original array (since the set of convex hull points is a subset of the original point set).}
1244 \cvarg{clockwise}{If true, the output convex hull will be oriented clockwise, otherwise it will be oriented counter-clockwise. Here, the usual screen coordinate system is assumed - the origin is at the top-left corner, x axis is oriented to the right, and y axis is oriented downwards.}
1247 The functions find the convex hull of a 2D point set using Sklansky's algorithm \cite{Sklansky82} that has $O(N logN)$ or $O(N)$ complexity (where $N$ is the number of input points), depending on how the initial sorting is implemented (currently it is $O(N logN)$. See the OpenCV sample \texttt{convexhull.c} that demonstrates the use of the different function variants.
1250 \cvCppFunc{fitEllipse}
1251 Fits an ellipse around a set of 2D points.
1253 \cvdefCpp{RotatedRect fitEllipse( const Mat\& points );}
1255 \cvarg{points}{The input 2D point set, represented by \texttt{CV\_32SC2} or \texttt{CV\_32FC2} matrix, or by \texttt{vector<Point>} or \texttt{vector<Point2f>} converted to the matrix using \texttt{Mat(const vector<T>\&)} constructor.}
1258 The function calculates the ellipse that fits best
1259 (in least-squares sense) a set of 2D points. It returns the rotated rectangle in which the ellipse is inscribed.
1262 Fits a line to a 2D or 3D point set.
1264 \cvdefCpp{void fitLine( const Mat\& points, Vec4f\& line, int distType,\par
1265 double param, double reps, double aeps );\newline
1266 void fitLine( const Mat\& points, Vec6f\& line, int distType,\par
1267 double param, double reps, double aeps );}
1269 \cvarg{points}{The input 2D point set, represented by \texttt{CV\_32SC2} or \texttt{CV\_32FC2} matrix, or by
1270 \texttt{vector<Point>}, \texttt{vector<Point2f>}, \texttt{vector<Point3i>} or \texttt{vector<Point3f>} converted to the matrix by \texttt{Mat(const vector<T>\&)} constructor}
1271 \cvarg{line}{The output line parameters. In the case of a 2d fitting,
1272 it is a vector of 4 floats \texttt{(vx, vy,
1273 x0, y0)} where \texttt{(vx, vy)} is a normalized vector collinear to the
1274 line and \texttt{(x0, y0)} is some point on the line. in the case of a
1275 3D fitting it is vector of 6 floats \texttt{(vx, vy, vz, x0, y0, z0)}
1276 where \texttt{(vx, vy, vz)} is a normalized vector collinear to the line
1277 and \texttt{(x0, y0, z0)} is some point on the line}
1278 \cvarg{distType}{The distance used by the M-estimator (see the discussion)}
1279 \cvarg{param}{Numerical parameter (\texttt{C}) for some types of distances, if 0 then some optimal value is chosen}
1280 \cvarg{reps, aeps}{Sufficient accuracy for the radius (distance between the coordinate origin and the line) and angle, respectively; 0.01 would be a good default value for both.}
1283 The functions \texttt{fitLine} fit a line to a 2D or 3D point set by minimizing $\sum_i \rho(r_i)$ where $r_i$ is the distance between the $i^{th}$ point and the line and $\rho(r)$ is a distance function, one of:
1286 \item[distType=CV\_DIST\_L2]
1287 \[ \rho(r) = r^2/2 \quad \text{(the simplest and the fastest least-squares method)} \]
1289 \item[distType=CV\_DIST\_L1]
1292 \item[distType=CV\_DIST\_L12]
1293 \[ \rho(r) = 2 \cdot (\sqrt{1 + \frac{r^2}{2}} - 1) \]
1295 \item[distType=CV\_DIST\_FAIR]
1296 \[ \rho\left(r\right) = C^2 \cdot \left( \frac{r}{C} - \log{\left(1 + \frac{r}{C}\right)}\right) \quad \text{where} \quad C=1.3998 \]
1298 \item[distType=CV\_DIST\_WELSCH]
1299 \[ \rho\left(r\right) = \frac{C^2}{2} \cdot \left( 1 - \exp{\left(-\left(\frac{r}{C}\right)^2\right)}\right) \quad \text{where} \quad C=2.9846 \]
1301 \item[distType=CV\_DIST\_HUBER]
1304 {C \cdot (r-C/2)}{otherwise} \quad \text{where} \quad C=1.345
1308 The algorithm is based on the M-estimator (\url{http://en.wikipedia.org/wiki/M-estimator}) technique, that iteratively fits the line using weighted least-squares algorithm and after each iteration the weights $w_i$ are adjusted to beinversely proportional to $\rho(r_i)$.
1311 \cvCppFunc{isContourConvex}
1312 Tests contour convexity.
1314 \cvdefCpp{bool isContourConvex( const Mat\& contour );}
1316 \cvarg{contour}{The tested contour, a matrix of type \texttt{CV\_32SC2} or \texttt{CV\_32FC2}, or \texttt{vector<Point>} or \texttt{vector<Point2f>} converted to the matrix using \texttt{Mat(const vector<T>\&)} constructor.}
1319 The function tests whether the input contour is convex or not. The contour must be simple, i.e. without self-intersections, otherwise the function output is undefined.
1322 \cvCppFunc{minAreaRect}
1323 Finds the minimum area rotated rectangle enclosing a 2D point set.
1325 \cvdefCpp{RotatedRect minAreaRect( const Mat\& points );}
1327 \cvarg{points}{The input 2D point set, represented by \texttt{CV\_32SC2} or \texttt{CV\_32FC2} matrix, or by \texttt{vector<Point>} or \texttt{vector<Point2f>} converted to the matrix using \texttt{Mat(const vector<T>\&)} constructor.}
1330 The function calculates and returns the minimum area bounding rectangle (possibly rotated) for the specified point set. See the OpenCV sample \texttt{minarea.c}
1332 \cvCppFunc{minEnclosingCircle}
1333 Finds the minimum area circle enclosing a 2D point set.
1335 \cvdefCpp{void minEnclosingCircle( const Mat\& points, Point2f\& center, float\& radius ); }
1337 \cvarg{points}{The input 2D point set, represented by \texttt{CV\_32SC2} or \texttt{CV\_32FC2} matrix, or by \texttt{vector<Point>} or \texttt{vector<Point2f>} converted to the matrix using \texttt{Mat(const vector<T>\&)} constructor.}
1338 \cvarg{center}{The output center of the circle}
1339 \cvarg{radius}{The output radius of the circle}
1342 The function finds the minimal enclosing circle of a 2D point set using iterative algorithm. See the OpenCV sample \texttt{minarea.c}
1344 \cvCppFunc{matchShapes}
1345 Compares two shapes.
1347 \cvdefCpp{double matchShapes( const Mat\& object1,\par
1348 const Mat\& object2,\par
1349 int method, double parameter=0 );}
1351 \cvarg{object1}{The first contour or grayscale image}
1352 \cvarg{object2}{The second contour or grayscale image}
1353 \cvarg{method}{Comparison method:
1354 \texttt{CV\_CONTOUR\_MATCH\_I1},\\
1355 \texttt{CV\_CONTOURS\_MATCH\_I2}\\
1357 \texttt{CV\_CONTOURS\_MATCH\_I3} (see the discussion below)}
1358 \cvarg{parameter}{Method-specific parameter (is not used now)}
1361 The function compares two shapes. The 3 implemented methods all use Hu invariants (see \cvCppCross{HuMoments}) as following ($A$ denotes \texttt{object1}, $B$ denotes \texttt{object2}):
1364 \item[method=CV\_CONTOUR\_MATCH\_I1]
1365 \[ I_1(A,B) = \sum_{i=1...7} \left| \frac{1}{m^A_i} - \frac{1}{m^B_i} \right| \]
1367 \item[method=CV\_CONTOUR\_MATCH\_I2]
1368 \[ I_2(A,B) = \sum_{i=1...7} \left| m^A_i - m^B_i \right| \]
1370 \item[method=CV\_CONTOUR\_MATCH\_I3]
1371 \[ I_3(A,B) = \sum_{i=1...7} \frac{ \left| m^A_i - m^B_i \right| }{ \left| m^A_i \right| } \]
1378 m^A_i = \mathrm{sign}(h^A_i) \cdot \log{h^A_i} \\
1379 m^B_i = \mathrm{sign}(h^B_i) \cdot \log{h^B_i}
1383 and $h^A_i, h^B_i$ are the Hu moments of $A$ and $B$ respectively.
1386 \cvCppFunc{pointPolygonTest}
1387 Performs point-in-contour test.
1389 \cvdefCpp{double pointPolygonTest( const Mat\& contour,\par
1390 Point2f pt, bool measureDist );}
1392 \cvarg{contour}{The input contour}
1393 \cvarg{pt}{The point tested against the contour}
1394 \cvarg{measureDist}{If true, the function estimates the signed distance from the point to the nearest contour edge; otherwise, the function only checks if the point is inside or not.}
1397 The function determines whether the
1398 point is inside a contour, outside, or lies on an edge (or coincides
1399 with a vertex). It returns positive (inside), negative (outside) or zero (on an edge) value,
1400 correspondingly. When \texttt{measureDist=false}, the return value
1401 is +1, -1 and 0, respectively. Otherwise, the return value
1402 it is a signed distance between the point and the nearest contour
1405 Here is the sample output of the function, where each image pixel is tested against the contour.
1407 \includegraphics[width=0.5\textwidth]{pics/pointpolygon.png}