\section{Clustering and Search in Multi-Dimensional Spaces} \ifCPy \cvCPyFunc{KMeans2} Splits set of vectors by a given number of clusters. \cvdefC{int cvKMeans2(const CvArr* samples, int nclusters,\par CvArr* labels, CvTermCriteria termcrit,\par int attempts=1, CvRNG* rng=0, \par int flags=0, CvArr* centers=0,\par double* compactness=0);} \cvdefPy{KMeans2(samples,nclusters,labels,termcrit)-> None} \begin{description} \cvarg{samples}{Floating-point matrix of input samples, one row per sample} \cvarg{nclusters}{Number of clusters to split the set by} \cvarg{labels}{Output integer vector storing cluster indices for every sample} \cvarg{termcrit}{Specifies maximum number of iterations and/or accuracy (distance the centers can move by between subsequent iterations)} \ifC \cvarg{attempts}{How many times the algorithm is executed using different initial labelings. The algorithm returns labels that yield the best compactness (see the last function parameter)} \cvarg{rng}{Optional external random number generator; can be used to fully control the function behaviour} \cvarg{flags}{Can be 0 or \texttt{CV\_KMEANS\_USE\_INITIAL\_LABELS}. The latter value means that during the first (and possibly the only) attempt, the function uses the user-supplied labels as the initial approximation instead of generating random labels. For the second and further attempts, the function will use randomly generated labels in any case} \cvarg{centers}{The optional output array of the cluster centers} \cvarg{compactness}{The optional output parameter, which is computed as $\sum_i ||\texttt{samples}_i - \texttt{centers}_{\texttt{labels}_i}||^2$ after every attempt; the best (minimum) value is chosen and the corresponding labels are returned by the function. Basically, the user can use only the core of the function, set the number of attempts to 1, initialize labels each time using a custom algorithm (\texttt{flags=CV\_KMEAN\_USE\_INITIAL\_LABELS}) and, based on the output compactness or any other criteria, choose the best clustering.} \fi \end{description} The function \texttt{cvKMeans2} implements a k-means algorithm that finds the centers of \texttt{nclusters} clusters and groups the input samples around the clusters. On output, $\texttt{labels}_i$ contains a cluster index for samples stored in the i-th row of the \texttt{samples} matrix. \ifC % Example: Clustering random samples of multi-gaussian distribution with k-means \begin{lstlisting} #include "cxcore.h" #include "highgui.h" void main( int argc, char** argv ) { #define MAX_CLUSTERS 5 CvScalar color_tab[MAX_CLUSTERS]; IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 ); CvRNG rng = cvRNG(0xffffffff); color_tab[0] = CV_RGB(255,0,0); color_tab[1] = CV_RGB(0,255,0); color_tab[2] = CV_RGB(100,100,255); color_tab[3] = CV_RGB(255,0,255); color_tab[4] = CV_RGB(255,255,0); cvNamedWindow( "clusters", 1 ); for(;;) { int k, cluster_count = cvRandInt(&rng)%MAX_CLUSTERS + 1; int i, sample_count = cvRandInt(&rng)%1000 + 1; CvMat* points = cvCreateMat( sample_count, 1, CV_32FC2 ); CvMat* clusters = cvCreateMat( sample_count, 1, CV_32SC1 ); /* generate random sample from multigaussian distribution */ for( k = 0; k < cluster_count; k++ ) { CvPoint center; CvMat point_chunk; center.x = cvRandInt(&rng)%img->width; center.y = cvRandInt(&rng)%img->height; cvGetRows( points, &point_chunk, k*sample_count/cluster_count, (k == (cluster_count - 1)) ? sample_count : (k+1)*sample_count/cluster_count ); cvRandArr( &rng, &point_chunk, CV_RAND_NORMAL, cvScalar(center.x,center.y,0,0), cvScalar(img->width/6, img->height/6,0,0) ); } /* shuffle samples */ for( i = 0; i < sample_count/2; i++ ) { CvPoint2D32f* pt1 = (CvPoint2D32f*)points->data.fl + cvRandInt(&rng)%sample_count; CvPoint2D32f* pt2 = (CvPoint2D32f*)points->data.fl + cvRandInt(&rng)%sample_count; CvPoint2D32f temp; CV_SWAP( *pt1, *pt2, temp ); } cvKMeans2( points, cluster_count, clusters, cvTermCriteria( CV_TERMCRIT_EPS+CV_TERMCRIT_ITER, 10, 1.0 )); cvZero( img ); for( i = 0; i < sample_count; i++ ) { CvPoint2D32f pt = ((CvPoint2D32f*)points->data.fl)[i]; int cluster_idx = clusters->data.i[i]; cvCircle( img, cvPointFrom32f(pt), 2, color_tab[cluster_idx], CV_FILLED ); } cvReleaseMat( &points ); cvReleaseMat( &clusters ); cvShowImage( "clusters", img ); int key = cvWaitKey(0); if( key == 27 ) break; } } \end{lstlisting} \cvCPyFunc{SeqPartition} Splits a sequence into equivalency classes. \cvdefC{ int cvSeqPartition( \par const CvSeq* seq,\par CvMemStorage* storage,\par CvSeq** labels,\par CvCmpFunc is\_equal,\par void* userdata ); } \begin{description} \cvarg{seq}{The sequence to partition} \cvarg{storage}{The storage block to store the sequence of equivalency classes. If it is NULL, the function uses \texttt{seq->storage} for output labels} \cvarg{labels}{Ouput parameter. Double pointer to the sequence of 0-based labels of input sequence elements} \cvarg{is\_equal}{The relation function that should return non-zero if the two particular sequence elements are from the same class, and zero otherwise. The partitioning algorithm uses transitive closure of the relation function as an equivalency critria} \cvarg{userdata}{Pointer that is transparently passed to the \texttt{is\_equal} function} \end{description} \begin{lstlisting} typedef int (CV_CDECL* CvCmpFunc)(const void* a, const void* b, void* userdata); \end{lstlisting} The function \texttt{cvSeqPartition} implements a quadratic algorithm for splitting a set into one or more equivalancy classes. The function returns the number of equivalency classes. % Example: Partitioning a 2d point set \begin{lstlisting} #include "cxcore.h" #include "highgui.h" #include CvSeq* point_seq = 0; IplImage* canvas = 0; CvScalar* colors = 0; int pos = 10; int is_equal( const void* _a, const void* _b, void* userdata ) { CvPoint a = *(const CvPoint*)_a; CvPoint b = *(const CvPoint*)_b; double threshold = *(double*)userdata; return (double)((a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y)) <= threshold; } void on_track( int pos ) { CvSeq* labels = 0; double threshold = pos*pos; int i, class_count = cvSeqPartition( point_seq, 0, &labels, is_equal, &threshold ); printf("%4d classes\n", class_count ); cvZero( canvas ); for( i = 0; i < labels->total; i++ ) { CvPoint pt = *(CvPoint*)cvGetSeqElem( point_seq, i ); CvScalar color = colors[*(int*)cvGetSeqElem( labels, i )]; cvCircle( canvas, pt, 1, color, -1 ); } cvShowImage( "points", canvas ); } int main( int argc, char** argv ) { CvMemStorage* storage = cvCreateMemStorage(0); point_seq = cvCreateSeq( CV_32SC2, sizeof(CvSeq), sizeof(CvPoint), storage ); CvRNG rng = cvRNG(0xffffffff); int width = 500, height = 500; int i, count = 1000; canvas = cvCreateImage( cvSize(width,height), 8, 3 ); colors = (CvScalar*)cvAlloc( count*sizeof(colors[0]) ); for( i = 0; i < count; i++ ) { CvPoint pt; int icolor; pt.x = cvRandInt( &rng ) % width; pt.y = cvRandInt( &rng ) % height; cvSeqPush( point_seq, &pt ); icolor = cvRandInt( &rng ) | 0x00404040; colors[i] = CV_RGB(icolor & 255, (icolor >> 8)&255, (icolor >> 16)&255); } cvNamedWindow( "points", 1 ); cvCreateTrackbar( "threshold", "points", &pos, 50, on_track ); on_track(pos); cvWaitKey(0); return 0; } \end{lstlisting} \fi \fi \ifCpp \cvCppFunc{kmeans} Finds the centers of clusters and groups the input samples around the clusters. \cvdefCpp{double kmeans( const Mat\& samples, int clusterCount, Mat\& labels,\par TermCriteria termcrit, int attempts,\par int flags, Mat* centers );} \begin{description} \cvarg{samples}{Floating-point matrix of input samples, one row per sample} \cvarg{clusterCount}{The number of clusters to split the set by} \cvarg{labels}{The input/output integer array that will store the cluster indices for every sample} \cvarg{termcrit}{Specifies maximum number of iterations and/or accuracy (distance the centers can move by between subsequent iterations)} \cvarg{attempts}{How many times the algorithm is executed using different initial labelings. The algorithm returns the labels that yield the best compactness (see the last function parameter)} \cvarg{flags}{It can take the following values: \begin{description} \cvarg{KMEANS\_RANDOM\_CENTERS}{Random initial centers are selected in each attempt} \cvarg{KMEANS\_PP\_CENTERS}{Use kmeans++ center initialization by Arthur and Vassilvitskii} \cvarg{KMEANS\_USE\_INITIAL\_LABELS}{During the first (and possibly the only) attempt, the function uses the user-supplied labels instaed of computing them from the initial centers. For the second and further attempts, the function will use the random or semi-random centers (use one of \texttt{KMEANS\_*\_CENTERS} flag to specify the exact method)} \end{description}} \cvarg{centers}{The output matrix of the cluster centers, one row per each cluster center} \end{description} The function \texttt{kmeans} implements a k-means algorithm that finds the centers of \texttt{clusterCount} clusters and groups the input samples around the clusters. On output, $\texttt{labels}_i$ contains a 0-based cluster index for the sample stored in the $i^{th}$ row of the \texttt{samples} matrix. The function returns the compactness measure, which is computed as \[ \sum_i \|\texttt{samples}_i - \texttt{centers}_{\texttt{labels}_i}\|^2 \] after every attempt; the best (minimum) value is chosen and the corresponding labels and the compactness value are returned by the function. Basically, the user can use only the core of the function, set the number of attempts to 1, initialize labels each time using some custom algorithm and pass them with \par (\texttt{flags}=\texttt{KMEANS\_USE\_INITIAL\_LABELS}) flag, and then choose the best (most-compact) clustering. \cvCppFunc{partition} Splits an element set into equivalency classes. \cvdefCpp{template int\newline partition( const vector<\_Tp>\& vec, vector\& labels,\par \_EqPredicate predicate=\_EqPredicate());} \begin{description} \cvarg{vec}{The set of elements stored as a vector} \cvarg{labels}{The output vector of labels; will contain as many elements as \texttt{vec}. Each label \texttt{labels[i]} is 0-based cluster index of \texttt{vec[i]}} \cvarg{predicate}{The equivalence predicate (i.e. pointer to a boolean function of two arguments or an instance of the class that has the method \texttt{bool operator()(const \_Tp\& a, const \_Tp\& b)}. The predicate returns true when the elements are certainly if the same class, and false if they may or may not be in the same class} \end{description} The generic function \texttt{partition} implements an $O(N^2)$ algorithm for splitting a set of $N$ elements into one or more equivalency classes, as described in \url{http://en.wikipedia.org/wiki/Disjoint-set_data_structure}. The function returns the number of equivalency classes. \subsection{Fast Approximate Nearest Neighbor Search} This section documents OpenCV's interface to the FLANN\footnote{http://people.cs.ubc.ca/\~mariusm/flann} library. FLANN (Fast Library for Approximate Nearest Neighbors) is a library that contains a collection of algorithms optimized for fast nearest neighbor search in large datasets and for high dimensional features. More information about FLANN can be found in \cite{muja_flann_2009}. \cvclass{cvflann::Index} The FLANN nearest neighbor index class. \begin{lstlisting} namespace cvflann { class Index { public: Index(const Mat& features, const IndexParams& params); void knnSearch(const vector& query, vector& indices, vector& dists, int knn, const SearchParams& params); void knnSearch(const Mat& queries, Mat& indices, Mat& dists, int knn, const SearchParams& params); int radiusSearch(const vector& query, vector& indices, vector& dists, float radius, const SearchParams& params); int radiusSearch(const Mat& query, Mat& indices, Mat& dists, float radius, const SearchParams& params); void save(std::string filename); int veclen() const; int size() const; }; } \end{lstlisting} \cvCppFunc{cvflann::Index::Index} Constructs a nearest neighbor search index for a given dataset. \cvdefCpp{Index::Index(const Mat\& features, const IndexParams\& params);} \begin{description} \cvarg{features}{ Matrix of type CV\_32F containing the features(points) to index. The size of the matrix is num\_features x feature\_dimensionality.} \cvarg{params}{Structure containing the index parameters. The type of index that will be constructed depends on the type of this parameter. The possible parameter types are:} \begin{description} \cvarg{LinearIndexParams}{When passing an object of this type, the index will perform a linear, brute-force search.} \begin{lstlisting} struct LinearIndexParams : public IndexParams { }; \end{lstlisting} \cvarg{KDTreeIndexParams}{When passing an object of this type the index constructed will consist of a set of randomized kd-trees which will be searched in parallel.} \begin{lstlisting} struct KDTreeIndexParams : public IndexParams { KDTreeIndexParams( int trees = 4 ); }; \end{lstlisting} \begin{description} \cvarg{trees}{The number of parallel kd-trees to use. Good values are in the range [1..16]} \end{description} \cvarg{KMeansIndexParams}{When passing an object of this type the index constructed will be a hierarchical k-means tree.} \begin{lstlisting} struct KMeansIndexParams : public IndexParams { KMeansIndexParams( int branching = 32, int iterations = 11, flann_centers_init_t centers_init = CENTERS_RANDOM, float cb_index = 0.2 ); }; \end{lstlisting} \begin{description} \cvarg{branching}{ The branching factor to use for the hierarchical k-means tree } \cvarg{iterations}{ The maximum number of iterations to use in the k-means clustering stage when building the k-means tree. A value of -1 used here means that the k-means clustering should be iterated until convergence} \cvarg{centers\_init}{The algorithm to use for selecting the initial centers when performing a k-means clustering step. The possible values are \texttt{CENTERS\_RANDOM} (picks the initial cluster centers randomly), \texttt{CENTERS\_GONZALES} (picks the initial centers using Gonzales' algorithm) and \texttt{CENTERS\_KMEANSPP} (picks the initial centers using the algorithm suggested in \cite{arthur_kmeanspp_2007})} \cvarg{cb\_index}{This parameter (cluster boundary index) influences the way exploration is performed in the hierarchical kmeans tree. When \texttt{cb\_index} is zero the next kmeans domain to be explored is choosen to be the one with the closest center. A value greater then zero also takes into account the size of the domain.} \end{description} \cvarg{CompositeIndexParams}{When using a parameters object of this type the index created combines the randomized kd-trees and the hierarchical k-means tree.} \begin{lstlisting} struct CompositeIndexParams : public IndexParams { CompositeIndexParams( int trees = 4, int branching = 32, int iterations = 11, flann_centers_init_t centers_init = CENTERS_RANDOM, float cb_index = 0.2 ); }; \end{lstlisting} \cvarg{AutotunedIndexParams}{When passing an object of this type the index created is automatically tuned to offer the best performance, by choosing the optimal index type (randomized kd-trees, hierarchical kmeans, linear) and parameters for the dataset provided.} \begin{lstlisting} struct AutotunedIndexParams : public IndexParams { AutotunedIndexParams( float target_precision = 0.9, float build_weight = 0.01, float memory_weight = 0, float sample_fraction = 0.1 ); }; \end{lstlisting} \begin{description} \cvarg{target\_precision}{ Is a number between 0 and 1 specifying the percentage of the approximate nearest-neighbor searches that return the exact nearest-neighbor. Using a higher value for this parameter gives more accurate results, but the search takes longer. The optimum value usually depends on the application. } \cvarg{build\_weight}{ Specifies the importance of the index build time raported to the nearest-neighbor search time. In some applications it's acceptable for the index build step to take a long time if the subsequent searches in the index can be performed very fast. In other applications it's required that the index be build as fast as possible even if that leads to slightly longer search times.} \cvarg{memory\_weight}{Is used to specify the tradeoff between time (index build time and search time) and memory used by the index. A value less than 1 gives more importance to the time spent and a value greater than 1 gives more importance to the memory usage.} \cvarg{sample\_fraction}{Is a number between 0 and 1 indicating what fraction of the dataset to use in the automatic parameter configuration algorithm. Running the algorithm on the full dataset gives the most accurate results, but for very large datasets can take longer than desired. In such case using just a fraction of the data helps speeding up this algorithm while still giving good approximations of the optimum parameters.} \end{description} \cvarg{SavedIndexParams}{This object type is used for loading a previously saved index from the disk.} \begin{lstlisting} struct SavedIndexParams : public IndexParams { SavedIndexParams( std::string filename ); }; \end{lstlisting} \begin{description} \cvarg{filename}{ The filename in which the index was saved. } \end{description} \end{description} \end{description} \cvCppFunc{cvflann::Index::knnSearch} Performs a K-nearest neighbor search for a given query point using the index. \cvdefCpp{void Index::knnSearch(const vector\& query, \par vector\& indices, \par vector\& dists, \par int knn, \par const SearchParams\& params);} \begin{description} \cvarg{query}{The query point} \cvarg{indices}{Vector that will contain the indices of the K-nearest neighbors found. It must have at least knn size.} \cvarg{dists}{Vector that will contain the distances to the K-nearest neighbors found. It must have at least knn size.} \cvarg{knn}{Number of nearest neighbors to search for.} \cvarg{params}{Search parameters} \begin{lstlisting} struct SearchParams { SearchParams(int checks = 32); }; \end{lstlisting} \begin{description} \cvarg{checks}{ The number of times the tree(s) in the index should be recursively traversed. A higher value for this parameter would give better search precision, but also take more time. If automatic configuration was used when the index was created, the number of checks required to achieve the specified precision was also computed, in which case this parameter is ignored.} \end{description} \end{description} \cvCppFunc{cvflann::Index::knnSearch} Performs a K-nearest neighbor search for multiple query points. \cvdefCpp{void Index::knnSearch(const Mat\& queries,\par Mat\& indices, Mat\& dists,\par int knn, const SearchParams\& params);} \begin{description} \cvarg{queries}{The query points, one per row} \cvarg{indices}{Indices of the nearest neighbors found } \cvarg{dists}{Distances to the nearest neighbors found} \cvarg{knn}{Number of nearest neighbors to search for} \cvarg{params}{Search parameters} \end{description} \cvCppFunc{cvflann::Index::radiusSearch} Performs a radius nearest neighbor search for a given query point. \cvdefCpp{int Index::radiusSearch(const vector\& query, \par vector\& indices, \par vector\& dists, \par float radius, \par const SearchParams\& params);} \begin{description} \cvarg{query}{The query point} \cvarg{indices}{Vector that will contain the indices of the points found within the search radius in decreasing order of the distance to the query point. If the number of neighbors in the search radius is bigger than the size of this vector, the ones that don't fit in the vector are ignored. } \cvarg{dists}{Vector that will contain the distances to the points found within the search radius} \cvarg{radius}{The search radius} \cvarg{params}{Search parameters} \end{description} \cvCppFunc{cvflann::Index::radiusSearch} Performs a radius nearest neighbor search for multiple query points. \cvdefCpp{int Index::radiusSearch(const Mat\& query, \par Mat\& indices, \par Mat\& dists, \par float radius, \par const SearchParams\& params);} \begin{description} \cvarg{queries}{The query points, one per row} \cvarg{indices}{Indices of the nearest neighbors found} \cvarg{dists}{Distances to the nearest neighbors found} \cvarg{radius}{The search radius} \cvarg{params}{Search parameters} \end{description} \cvCppFunc{cvflann::Index::save} Saves the index to a file. \cvdefCpp{void Index::save(std::string filename);} \begin{description} \cvarg{filename}{The file to save the index to} \end{description} \cvCppFunc{cvflann::hierarchicalClustering} Clusters the given points by constructing a hierarchical k-means tree and choosing a cut in the tree that minimizes the cluster's variance. \cvdefCpp{int hierarchicalClustering(const Mat\& features, Mat\& centers,\par const KMeansIndexParams\& params);} \begin{description} \cvarg{features}{The points to be clustered} \cvarg{centers}{The centers of the clusters obtained. The number of rows in this matrix represents the number of clusters desired, however, because of the way the cut in the hierarchical tree is chosen, the number of clusters computed will be the highest number of the form \texttt{(branching-1)*k+1} that's lower than the number of clusters desired, where \texttt{branching} is the tree's branching factor (see description of the KMeansIndexParams).} \cvarg{params}{Parameters used in the construction of the hierarchical k-means tree} \end{description} The function returns the number of clusters computed. \fi