/****************************************************************************** ** Filename: intmatcher.c ** Purpose: Generic high level classification routines. ** Author: Robert Moss ** History: Wed Feb 13 17:35:28 MST 1991, RWM, Created. ** Mon Mar 11 16:33:02 MST 1991, RWM, Modified to add ** support for adaptive matching. ** (c) Copyright Hewlett-Packard Company, 1988. ** Licensed under the Apache License, Version 2.0 (the "License"); ** you may not use this file except in compliance with the License. ** You may obtain a copy of the License at ** http://www.apache.org/licenses/LICENSE-2.0 ** Unless required by applicable law or agreed to in writing, software ** distributed under the License is distributed on an "AS IS" BASIS, ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. ** See the License for the specific language governing permissions and ** limitations under the License. ******************************************************************************/ // Include automatically generated configuration file if running autoconf. #ifdef HAVE_CONFIG_H #include "config_auto.h" #endif /*---------------------------------------------------------------------------- Include Files and Type Defines ----------------------------------------------------------------------------*/ #include "intmatcher.h" #include "fontinfo.h" #include "intproto.h" #include "callcpp.h" #include "scrollview.h" #include "float2int.h" #include "globals.h" #include "helpers.h" #include "classify.h" #include "shapetable.h" #include using tesseract::ScoredFont; using tesseract::UnicharRating; /*---------------------------------------------------------------------------- Global Data Definitions and Declarations ----------------------------------------------------------------------------*/ // Parameters of the sigmoid used to convert similarity to evidence in the // similarity_evidence_table_ that is used to convert distance metric to an // 8 bit evidence value in the secondary matcher. (See IntMatcher::Init). const float IntegerMatcher::kSEExponentialMultiplier = 0.0; const float IntegerMatcher::kSimilarityCenter = 0.0075; #define offset_table_entries \ 255, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, \ 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, \ 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, \ 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, \ 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, \ 0, 1, 0, 2, 0, 1, 0, 7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, \ 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, \ 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, \ 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, \ 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, \ 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 #define INTMATCHER_OFFSET_TABLE_SIZE 256 #define next_table_entries \ 0, 0, 0, 0x2, 0, 0x4, 0x4, 0x6, 0, 0x8, 0x8, 0x0a, 0x08, 0x0c, 0x0c, 0x0e, \ 0, 0x10, 0x10, 0x12, 0x10, 0x14, 0x14, 0x16, 0x10, 0x18, 0x18, 0x1a, \ 0x18, 0x1c, 0x1c, 0x1e, 0, 0x20, 0x20, 0x22, 0x20, 0x24, 0x24, 0x26, \ 0x20, 0x28, 0x28, 0x2a, 0x28, 0x2c, 0x2c, 0x2e, 0x20, 0x30, 0x30, 0x32, \ 0x30, 0x34, 0x34, 0x36, 0x30, 0x38, 0x38, 0x3a, 0x38, 0x3c, 0x3c, 0x3e, \ 0, 0x40, 0x40, 0x42, 0x40, 0x44, 0x44, 0x46, 0x40, 0x48, 0x48, 0x4a, \ 0x48, 0x4c, 0x4c, 0x4e, 0x40, 0x50, 0x50, 0x52, 0x50, 0x54, 0x54, 0x56, \ 0x50, 0x58, 0x58, 0x5a, 0x58, 0x5c, 0x5c, 0x5e, 0x40, 0x60, 0x60, 0x62, \ 0x60, 0x64, 0x64, 0x66, 0x60, 0x68, 0x68, 0x6a, 0x68, 0x6c, 0x6c, 0x6e, \ 0x60, 0x70, 0x70, 0x72, 0x70, 0x74, 0x74, 0x76, 0x70, 0x78, 0x78, 0x7a, \ 0x78, 0x7c, 0x7c, 0x7e, 0, 0x80, 0x80, 0x82, 0x80, 0x84, 0x84, 0x86, \ 0x80, 0x88, 0x88, 0x8a, 0x88, 0x8c, 0x8c, 0x8e, 0x80, 0x90, 0x90, 0x92, \ 0x90, 0x94, 0x94, 0x96, 0x90, 0x98, 0x98, 0x9a, 0x98, 0x9c, 0x9c, 0x9e, \ 0x80, 0xa0, 0xa0, 0xa2, 0xa0, 0xa4, 0xa4, 0xa6, 0xa0, 0xa8, 0xa8, 0xaa, \ 0xa8, 0xac, 0xac, 0xae, 0xa0, 0xb0, 0xb0, 0xb2, 0xb0, 0xb4, 0xb4, 0xb6, \ 0xb0, 0xb8, 0xb8, 0xba, 0xb8, 0xbc, 0xbc, 0xbe, 0x80, 0xc0, 0xc0, 0xc2, \ 0xc0, 0xc4, 0xc4, 0xc6, 0xc0, 0xc8, 0xc8, 0xca, 0xc8, 0xcc, 0xcc, 0xce, \ 0xc0, 0xd0, 0xd0, 0xd2, 0xd0, 0xd4, 0xd4, 0xd6, 0xd0, 0xd8, 0xd8, 0xda, \ 0xd8, 0xdc, 0xdc, 0xde, 0xc0, 0xe0, 0xe0, 0xe2, 0xe0, 0xe4, 0xe4, 0xe6, \ 0xe0, 0xe8, 0xe8, 0xea, 0xe8, 0xec, 0xec, 0xee, 0xe0, 0xf0, 0xf0, 0xf2, \ 0xf0, 0xf4, 0xf4, 0xf6, 0xf0, 0xf8, 0xf8, 0xfa, 0xf8, 0xfc, 0xfc, 0xfe // See http://b/19318793 (#6) for a complete discussion. Merging arrays // offset_table and next_table helps improve performance of PIE code. static const uinT8 data_table[512] = {offset_table_entries, next_table_entries}; static const uinT8* const offset_table = &data_table[0]; static const uinT8* const next_table = &data_table[INTMATCHER_OFFSET_TABLE_SIZE]; namespace tesseract { // Encapsulation of the intermediate data and computations made by the class // pruner. The class pruner implements a simple linear classifier on binary // features by heavily quantizing the feature space, and applying // NUM_BITS_PER_CLASS (2)-bit weights to the features. Lack of resolution in // weights is compensated by a non-constant bias that is dependent on the // number of features present. class ClassPruner { public: ClassPruner(int max_classes) { // The unrolled loop in ComputeScores means that the array sizes need to // be rounded up so that the array is big enough to accommodate the extra // entries accessed by the unrolling. Each pruner word is of sized // BITS_PER_WERD and each entry is NUM_BITS_PER_CLASS, so there are // BITS_PER_WERD / NUM_BITS_PER_CLASS entries. // See ComputeScores. max_classes_ = max_classes; rounded_classes_ = RoundUp( max_classes, WERDS_PER_CP_VECTOR * BITS_PER_WERD / NUM_BITS_PER_CLASS); class_count_ = new int[rounded_classes_]; norm_count_ = new int[rounded_classes_]; sort_key_ = new int[rounded_classes_ + 1]; sort_index_ = new int[rounded_classes_ + 1]; for (int i = 0; i < rounded_classes_; i++) { class_count_[i] = 0; } pruning_threshold_ = 0; num_features_ = 0; num_classes_ = 0; } ~ClassPruner() { delete []class_count_; delete []norm_count_; delete []sort_key_; delete []sort_index_; } /// Computes the scores for every class in the character set, by summing the /// weights for each feature and stores the sums internally in class_count_. void ComputeScores(const INT_TEMPLATES_STRUCT* int_templates, int num_features, const INT_FEATURE_STRUCT* features) { num_features_ = num_features; int num_pruners = int_templates->NumClassPruners; for (int f = 0; f < num_features; ++f) { const INT_FEATURE_STRUCT* feature = &features[f]; // Quantize the feature to NUM_CP_BUCKETS*NUM_CP_BUCKETS*NUM_CP_BUCKETS. int x = feature->X * NUM_CP_BUCKETS >> 8; int y = feature->Y * NUM_CP_BUCKETS >> 8; int theta = feature->Theta * NUM_CP_BUCKETS >> 8; int class_id = 0; // Each CLASS_PRUNER_STRUCT only covers CLASSES_PER_CP(32) classes, so // we need a collection of them, indexed by pruner_set. for (int pruner_set = 0; pruner_set < num_pruners; ++pruner_set) { // Look up quantized feature in a 3-D array, an array of weights for // each class. const uinT32* pruner_word_ptr = int_templates->ClassPruners[pruner_set]->p[x][y][theta]; for (int word = 0; word < WERDS_PER_CP_VECTOR; ++word) { uinT32 pruner_word = *pruner_word_ptr++; // This inner loop is unrolled to speed up the ClassPruner. // Currently gcc would not unroll it unless it is set to O3 // level of optimization or -funroll-loops is specified. /* uinT32 class_mask = (1 << NUM_BITS_PER_CLASS) - 1; for (int bit = 0; bit < BITS_PER_WERD/NUM_BITS_PER_CLASS; bit++) { class_count_[class_id++] += pruner_word & class_mask; pruner_word >>= NUM_BITS_PER_CLASS; } */ class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; pruner_word >>= NUM_BITS_PER_CLASS; class_count_[class_id++] += pruner_word & CLASS_PRUNER_CLASS_MASK; } } } } /// Adjusts the scores according to the number of expected features. Used /// in lieu of a constant bias, this penalizes classes that expect more /// features than there are present. Thus an actual c will score higher for c /// than e, even though almost all the features match e as well as c, because /// e expects more features to be present. void AdjustForExpectedNumFeatures(const uinT16* expected_num_features, int cutoff_strength) { for (int class_id = 0; class_id < max_classes_; ++class_id) { if (num_features_ < expected_num_features[class_id]) { int deficit = expected_num_features[class_id] - num_features_; class_count_[class_id] -= class_count_[class_id] * deficit / (num_features_ * cutoff_strength + deficit); } } } /// Zeros the scores for classes disabled in the unicharset. /// Implements the black-list to recognize a subset of the character set. void DisableDisabledClasses(const UNICHARSET& unicharset) { for (int class_id = 0; class_id < max_classes_; ++class_id) { if (!unicharset.get_enabled(class_id)) class_count_[class_id] = 0; // This char is disabled! } } /** Zeros the scores of fragments. */ void DisableFragments(const UNICHARSET& unicharset) { for (int class_id = 0; class_id < max_classes_; ++class_id) { // Do not include character fragments in the class pruner // results if disable_character_fragments is true. if (unicharset.get_fragment(class_id)) { class_count_[class_id] = 0; } } } /// Normalizes the counts for xheight, putting the normalized result in /// norm_count_. Applies a simple subtractive penalty for incorrect vertical /// position provided by the normalization_factors array, indexed by /// character class, and scaled by the norm_multiplier. void NormalizeForXheight(int norm_multiplier, const uinT8* normalization_factors) { for (int class_id = 0; class_id < max_classes_; class_id++) { norm_count_[class_id] = class_count_[class_id] - ((norm_multiplier * normalization_factors[class_id]) >> 8); } } /** The nop normalization copies the class_count_ array to norm_count_. */ void NoNormalization() { for (int class_id = 0; class_id < max_classes_; class_id++) { norm_count_[class_id] = class_count_[class_id]; } } /// Prunes the classes using <the maximum count> * pruning_factor/256 as a /// threshold for keeping classes. If max_of_non_fragments, then ignore /// fragments in computing the maximum count. void PruneAndSort(int pruning_factor, int keep_this, bool max_of_non_fragments, const UNICHARSET& unicharset) { int max_count = 0; for (int c = 0; c < max_classes_; ++c) { if (norm_count_[c] > max_count && // This additional check is added in order to ensure that // the classifier will return at least one non-fragmented // character match. // TODO(daria): verify that this helps accuracy and does not // hurt performance. (!max_of_non_fragments || !unicharset.get_fragment(c))) { max_count = norm_count_[c]; } } // Prune Classes. pruning_threshold_ = (max_count * pruning_factor) >> 8; // Select Classes. if (pruning_threshold_ < 1) pruning_threshold_ = 1; num_classes_ = 0; for (int class_id = 0; class_id < max_classes_; class_id++) { if (norm_count_[class_id] >= pruning_threshold_ || class_id == keep_this) { ++num_classes_; sort_index_[num_classes_] = class_id; sort_key_[num_classes_] = norm_count_[class_id]; } } // Sort Classes using Heapsort Algorithm. if (num_classes_ > 1) HeapSort(num_classes_, sort_key_, sort_index_); } /** Prints debug info on the class pruner matches for the pruned classes only. */ void DebugMatch(const Classify& classify, const INT_TEMPLATES_STRUCT* int_templates, const INT_FEATURE_STRUCT* features) const { int num_pruners = int_templates->NumClassPruners; int max_num_classes = int_templates->NumClasses; for (int f = 0; f < num_features_; ++f) { const INT_FEATURE_STRUCT* feature = &features[f]; tprintf("F=%3d(%d,%d,%d),", f, feature->X, feature->Y, feature->Theta); // Quantize the feature to NUM_CP_BUCKETS*NUM_CP_BUCKETS*NUM_CP_BUCKETS. int x = feature->X * NUM_CP_BUCKETS >> 8; int y = feature->Y * NUM_CP_BUCKETS >> 8; int theta = feature->Theta * NUM_CP_BUCKETS >> 8; int class_id = 0; for (int pruner_set = 0; pruner_set < num_pruners; ++pruner_set) { // Look up quantized feature in a 3-D array, an array of weights for // each class. const uinT32* pruner_word_ptr = int_templates->ClassPruners[pruner_set]->p[x][y][theta]; for (int word = 0; word < WERDS_PER_CP_VECTOR; ++word) { uinT32 pruner_word = *pruner_word_ptr++; for (int word_class = 0; word_class < 16 && class_id < max_num_classes; ++word_class, ++class_id) { if (norm_count_[class_id] >= pruning_threshold_) { tprintf(" %s=%d,", classify.ClassIDToDebugStr(int_templates, class_id, 0).string(), pruner_word & CLASS_PRUNER_CLASS_MASK); } pruner_word >>= NUM_BITS_PER_CLASS; } } tprintf("\n"); } } } /** Prints a summary of the pruner result. */ void SummarizeResult(const Classify& classify, const INT_TEMPLATES_STRUCT* int_templates, const uinT16* expected_num_features, int norm_multiplier, const uinT8* normalization_factors) const { tprintf("CP:%d classes, %d features:\n", num_classes_, num_features_); for (int i = 0; i < num_classes_; ++i) { int class_id = sort_index_[num_classes_ - i]; STRING class_string = classify.ClassIDToDebugStr(int_templates, class_id, 0); tprintf("%s:Initial=%d, E=%d, Xht-adj=%d, N=%d, Rat=%.2f\n", class_string.string(), class_count_[class_id], expected_num_features[class_id], (norm_multiplier * normalization_factors[class_id]) >> 8, sort_key_[num_classes_ - i], 100.0 - 100.0 * sort_key_[num_classes_ - i] / (CLASS_PRUNER_CLASS_MASK * num_features_)); } } /// Copies the pruned, sorted classes into the output results and returns /// the number of classes. int SetupResults(GenericVector* results) const { CP_RESULT_STRUCT empty; results->init_to_size(num_classes_, empty); for (int c = 0; c < num_classes_; ++c) { (*results)[c].Class = sort_index_[num_classes_ - c]; (*results)[c].Rating = 1.0 - sort_key_[num_classes_ - c] / (static_cast(CLASS_PRUNER_CLASS_MASK) * num_features_); } return num_classes_; } private: /** Array[rounded_classes_] of initial counts for each class. */ int *class_count_; /// Array[rounded_classes_] of modified counts for each class after normalizing /// for expected number of features, disabled classes, fragments, and xheights. int *norm_count_; /** Array[rounded_classes_ +1] of pruned counts that gets sorted */ int *sort_key_; /** Array[rounded_classes_ +1] of classes corresponding to sort_key_. */ int *sort_index_; /** Number of classes in this class pruner. */ int max_classes_; /** Rounded up number of classes used for array sizes. */ int rounded_classes_; /** Threshold count applied to prune classes. */ int pruning_threshold_; /** The number of features used to compute the scores. */ int num_features_; /** Final number of pruned classes. */ int num_classes_; }; /*---------------------------------------------------------------------------- Public Code ----------------------------------------------------------------------------*/ /** * Runs the class pruner from int_templates on the given features, returning * the number of classes output in results. * @param int_templates Class pruner tables * @param num_features Number of features in blob * @param features Array of features * @param normalization_factors Array of fudge factors from blob * normalization process (by CLASS_INDEX) * @param expected_num_features Array of expected number of features * for each class (by CLASS_INDEX) * @param results Sorted Array of pruned classes. Must be an array * of size at least int_templates->NumClasses. * @param keep_this */ int Classify::PruneClasses(const INT_TEMPLATES_STRUCT* int_templates, int num_features, int keep_this, const INT_FEATURE_STRUCT* features, const uinT8* normalization_factors, const uinT16* expected_num_features, GenericVector* results) { ClassPruner pruner(int_templates->NumClasses); // Compute initial match scores for all classes. pruner.ComputeScores(int_templates, num_features, features); // Adjust match scores for number of expected features. pruner.AdjustForExpectedNumFeatures(expected_num_features, classify_cp_cutoff_strength); // Apply disabled classes in unicharset - only works without a shape_table. if (shape_table_ == NULL) pruner.DisableDisabledClasses(unicharset); // If fragments are disabled, remove them, also only without a shape table. if (disable_character_fragments && shape_table_ == NULL) pruner.DisableFragments(unicharset); // If we have good x-heights, apply the given normalization factors. if (normalization_factors != NULL) { pruner.NormalizeForXheight(classify_class_pruner_multiplier, normalization_factors); } else { pruner.NoNormalization(); } // Do the actual pruning and sort the short-list. pruner.PruneAndSort(classify_class_pruner_threshold, keep_this, shape_table_ == NULL, unicharset); if (classify_debug_level > 2) { pruner.DebugMatch(*this, int_templates, features); } if (classify_debug_level > 1) { pruner.SummarizeResult(*this, int_templates, expected_num_features, classify_class_pruner_multiplier, normalization_factors); } // Convert to the expected output format. return pruner.SetupResults(results); } } // namespace tesseract /** * IntegerMatcher returns the best configuration and rating * for a single class. The class matched against is determined * by the uniqueness of the ClassTemplate parameter. The * best rating and its associated configuration are returned. * * Globals: * - local_matcher_multiplier_ Normalization factor multiplier * param ClassTemplate Prototypes & tables for a class * param BlobLength Length of unormalized blob * param NumFeatures Number of features in blob * param Features Array of features * param NormalizationFactor Fudge factor from blob normalization process * param Result Class rating & configuration: (0.0 -> 1.0), 0=bad, 1=good * param Debug Debugger flag: 1=debugger on * @return none * @note Exceptions: none * @note History: Tue Feb 19 16:36:23 MST 1991, RWM, Created. */ void IntegerMatcher::Match(INT_CLASS ClassTemplate, BIT_VECTOR ProtoMask, BIT_VECTOR ConfigMask, inT16 NumFeatures, const INT_FEATURE_STRUCT* Features, UnicharRating* Result, int AdaptFeatureThreshold, int Debug, bool SeparateDebugWindows) { ScratchEvidence *tables = new ScratchEvidence(); int Feature; int BestMatch; if (MatchDebuggingOn (Debug)) cprintf ("Integer Matcher -------------------------------------------\n"); tables->Clear(ClassTemplate); Result->feature_misses = 0; for (Feature = 0; Feature < NumFeatures; Feature++) { int csum = UpdateTablesForFeature(ClassTemplate, ProtoMask, ConfigMask, Feature, &Features[Feature], tables, Debug); // Count features that were missed over all configs. if (csum == 0) ++Result->feature_misses; } #ifndef GRAPHICS_DISABLED if (PrintProtoMatchesOn(Debug) || PrintMatchSummaryOn(Debug)) { DebugFeatureProtoError(ClassTemplate, ProtoMask, ConfigMask, *tables, NumFeatures, Debug); } if (DisplayProtoMatchesOn(Debug)) { DisplayProtoDebugInfo(ClassTemplate, ProtoMask, ConfigMask, *tables, SeparateDebugWindows); } if (DisplayFeatureMatchesOn(Debug)) { DisplayFeatureDebugInfo(ClassTemplate, ProtoMask, ConfigMask, NumFeatures, Features, AdaptFeatureThreshold, Debug, SeparateDebugWindows); } #endif tables->UpdateSumOfProtoEvidences(ClassTemplate, ConfigMask, NumFeatures); tables->NormalizeSums(ClassTemplate, NumFeatures, NumFeatures); BestMatch = FindBestMatch(ClassTemplate, *tables, Result); #ifndef GRAPHICS_DISABLED if (PrintMatchSummaryOn(Debug)) Result->Print(); if (MatchDebuggingOn(Debug)) cprintf("Match Complete --------------------------------------------\n"); #endif delete tables; } /** * FindGoodProtos finds all protos whose normalized proto-evidence * exceed classify_adapt_proto_thresh. The list is ordered by increasing * proto id number. * * Globals: * - local_matcher_multiplier_ Normalization factor multiplier * param ClassTemplate Prototypes & tables for a class * param ProtoMask AND Mask for proto word * param ConfigMask AND Mask for config word * param BlobLength Length of unormalized blob * param NumFeatures Number of features in blob * param Features Array of features * param ProtoArray Array of good protos * param AdaptProtoThreshold Threshold for good protos * param Debug Debugger flag: 1=debugger on * @return Number of good protos in ProtoArray. * @note Exceptions: none * @note History: Tue Mar 12 17:09:26 MST 1991, RWM, Created */ int IntegerMatcher::FindGoodProtos( INT_CLASS ClassTemplate, BIT_VECTOR ProtoMask, BIT_VECTOR ConfigMask, uinT16 BlobLength, inT16 NumFeatures, INT_FEATURE_ARRAY Features, PROTO_ID *ProtoArray, int AdaptProtoThreshold, int Debug) { ScratchEvidence *tables = new ScratchEvidence(); int NumGoodProtos = 0; /* DEBUG opening heading */ if (MatchDebuggingOn (Debug)) cprintf ("Find Good Protos -------------------------------------------\n"); tables->Clear(ClassTemplate); for (int Feature = 0; Feature < NumFeatures; Feature++) UpdateTablesForFeature( ClassTemplate, ProtoMask, ConfigMask, Feature, &(Features[Feature]), tables, Debug); #ifndef GRAPHICS_DISABLED if (PrintProtoMatchesOn (Debug) || PrintMatchSummaryOn (Debug)) DebugFeatureProtoError(ClassTemplate, ProtoMask, ConfigMask, *tables, NumFeatures, Debug); #endif /* Average Proto Evidences & Find Good Protos */ for (int proto = 0; proto < ClassTemplate->NumProtos; proto++) { /* Compute Average for Actual Proto */ int Temp = 0; for (int i = 0; i < ClassTemplate->ProtoLengths[proto]; i++) Temp += tables->proto_evidence_[proto][i]; Temp /= ClassTemplate->ProtoLengths[proto]; /* Find Good Protos */ if (Temp >= AdaptProtoThreshold) { *ProtoArray = proto; ProtoArray++; NumGoodProtos++; } } if (MatchDebuggingOn (Debug)) cprintf ("Match Complete --------------------------------------------\n"); delete tables; return NumGoodProtos; } /** * FindBadFeatures finds all features with maximum feature-evidence < * AdaptFeatureThresh. The list is ordered by increasing feature number. * @param ClassTemplate Prototypes & tables for a class * @param ProtoMask AND Mask for proto word * @param ConfigMask AND Mask for config word * @param BlobLength Length of unormalized blob * @param NumFeatures Number of features in blob * @param Features Array of features * @param FeatureArray Array of bad features * @param AdaptFeatureThreshold Threshold for bad features * @param Debug Debugger flag: 1=debugger on * @return Number of bad features in FeatureArray. * @note History: Tue Mar 12 17:09:26 MST 1991, RWM, Created */ int IntegerMatcher::FindBadFeatures( INT_CLASS ClassTemplate, BIT_VECTOR ProtoMask, BIT_VECTOR ConfigMask, uinT16 BlobLength, inT16 NumFeatures, INT_FEATURE_ARRAY Features, FEATURE_ID *FeatureArray, int AdaptFeatureThreshold, int Debug) { ScratchEvidence *tables = new ScratchEvidence(); int NumBadFeatures = 0; /* DEBUG opening heading */ if (MatchDebuggingOn(Debug)) cprintf("Find Bad Features -------------------------------------------\n"); tables->Clear(ClassTemplate); for (int Feature = 0; Feature < NumFeatures; Feature++) { UpdateTablesForFeature( ClassTemplate, ProtoMask, ConfigMask, Feature, &Features[Feature], tables, Debug); /* Find Best Evidence for Current Feature */ int best = 0; for (int i = 0; i < ClassTemplate->NumConfigs; i++) if (tables->feature_evidence_[i] > best) best = tables->feature_evidence_[i]; /* Find Bad Features */ if (best < AdaptFeatureThreshold) { *FeatureArray = Feature; FeatureArray++; NumBadFeatures++; } } #ifndef GRAPHICS_DISABLED if (PrintProtoMatchesOn(Debug) || PrintMatchSummaryOn(Debug)) DebugFeatureProtoError(ClassTemplate, ProtoMask, ConfigMask, *tables, NumFeatures, Debug); #endif if (MatchDebuggingOn(Debug)) cprintf("Match Complete --------------------------------------------\n"); delete tables; return NumBadFeatures; } void IntegerMatcher::Init(tesseract::IntParam *classify_debug_level) { classify_debug_level_ = classify_debug_level; /* Initialize table for evidence to similarity lookup */ for (int i = 0; i < SE_TABLE_SIZE; i++) { uinT32 IntSimilarity = i << (27 - SE_TABLE_BITS); double Similarity = ((double) IntSimilarity) / 65536.0 / 65536.0; double evidence = Similarity / kSimilarityCenter; evidence = 255.0 / (evidence * evidence + 1.0); if (kSEExponentialMultiplier > 0.0) { double scale = 1.0 - exp(-kSEExponentialMultiplier) * exp(kSEExponentialMultiplier * ((double) i / SE_TABLE_SIZE)); evidence *= ClipToRange(scale, 0.0, 1.0); } similarity_evidence_table_[i] = (uinT8) (evidence + 0.5); } /* Initialize evidence computation variables */ evidence_table_mask_ = ((1 << kEvidenceTableBits) - 1) << (9 - kEvidenceTableBits); mult_trunc_shift_bits_ = (14 - kIntEvidenceTruncBits); table_trunc_shift_bits_ = (27 - SE_TABLE_BITS - (mult_trunc_shift_bits_ << 1)); evidence_mult_mask_ = ((1 << kIntEvidenceTruncBits) - 1); } /*---------------------------------------------------------------------------- Private Code ----------------------------------------------------------------------------*/ void ScratchEvidence::Clear(const INT_CLASS class_template) { memset(sum_feature_evidence_, 0, class_template->NumConfigs * sizeof(sum_feature_evidence_[0])); memset(proto_evidence_, 0, class_template->NumProtos * sizeof(proto_evidence_[0])); } void ScratchEvidence::ClearFeatureEvidence(const INT_CLASS class_template) { memset(feature_evidence_, 0, class_template->NumConfigs * sizeof(feature_evidence_[0])); } /** * Print debugging information for Configuations * @return none * @note Exceptions: none * @note History: Wed Feb 27 14:12:28 MST 1991, RWM, Created. */ void IMDebugConfiguration(int FeatureNum, uinT16 ActualProtoNum, uinT8 Evidence, BIT_VECTOR ConfigMask, uinT32 ConfigWord) { cprintf ("F = %3d, P = %3d, E = %3d, Configs = ", FeatureNum, (int) ActualProtoNum, (int) Evidence); while (ConfigWord) { if (ConfigWord & 1) cprintf ("1"); else cprintf ("0"); ConfigWord >>= 1; } cprintf ("\n"); } /** * Print debugging information for Configuations * @return none * @note Exceptions: none * @note History: Wed Feb 27 14:12:28 MST 1991, RWM, Created. */ void IMDebugConfigurationSum(int FeatureNum, uinT8 *FeatureEvidence, inT32 ConfigCount) { cprintf("F=%3d, C=", FeatureNum); for (int ConfigNum = 0; ConfigNum < ConfigCount; ConfigNum++) { cprintf("%4d", FeatureEvidence[ConfigNum]); } cprintf("\n"); } /** * For the given feature: prune protos, compute evidence, * update Feature Evidence, Proto Evidence, and Sum of Feature * Evidence tables. * @param ClassTemplate Prototypes & tables for a class * @param FeatureNum Current feature number (for DEBUG only) * @param Feature Pointer to a feature struct * @param tables Evidence tables * @param Debug Debugger flag: 1=debugger on * @return none */ int IntegerMatcher::UpdateTablesForFeature( INT_CLASS ClassTemplate, BIT_VECTOR ProtoMask, BIT_VECTOR ConfigMask, int FeatureNum, const INT_FEATURE_STRUCT* Feature, ScratchEvidence *tables, int Debug) { register uinT32 ConfigWord; register uinT32 ProtoWord; register uinT32 ProtoNum; register uinT32 ActualProtoNum; uinT8 proto_byte; inT32 proto_word_offset; inT32 proto_offset; uinT8 config_byte; inT32 config_offset; PROTO_SET ProtoSet; uinT32 *ProtoPrunerPtr; INT_PROTO Proto; int ProtoSetIndex; uinT8 Evidence; uinT32 XFeatureAddress; uinT32 YFeatureAddress; uinT32 ThetaFeatureAddress; register uinT8 *UINT8Pointer; register int ProtoIndex; uinT8 Temp; register int *IntPointer; int ConfigNum; register inT32 M3; register inT32 A3; register uinT32 A4; tables->ClearFeatureEvidence(ClassTemplate); /* Precompute Feature Address offset for Proto Pruning */ XFeatureAddress = ((Feature->X >> 2) << 1); YFeatureAddress = (NUM_PP_BUCKETS << 1) + ((Feature->Y >> 2) << 1); ThetaFeatureAddress = (NUM_PP_BUCKETS << 2) + ((Feature->Theta >> 2) << 1); for (ProtoSetIndex = 0, ActualProtoNum = 0; ProtoSetIndex < ClassTemplate->NumProtoSets; ProtoSetIndex++) { ProtoSet = ClassTemplate->ProtoSets[ProtoSetIndex]; ProtoPrunerPtr = (uinT32 *) ((*ProtoSet).ProtoPruner); for (ProtoNum = 0; ProtoNum < PROTOS_PER_PROTO_SET; ProtoNum += (PROTOS_PER_PROTO_SET >> 1), ActualProtoNum += (PROTOS_PER_PROTO_SET >> 1), ProtoMask++, ProtoPrunerPtr++) { /* Prune Protos of current Proto Set */ ProtoWord = *(ProtoPrunerPtr + XFeatureAddress); ProtoWord &= *(ProtoPrunerPtr + YFeatureAddress); ProtoWord &= *(ProtoPrunerPtr + ThetaFeatureAddress); ProtoWord &= *ProtoMask; if (ProtoWord != 0) { proto_byte = ProtoWord & 0xff; ProtoWord >>= 8; proto_word_offset = 0; while (ProtoWord != 0 || proto_byte != 0) { while (proto_byte == 0) { proto_byte = ProtoWord & 0xff; ProtoWord >>= 8; proto_word_offset += 8; } proto_offset = offset_table[proto_byte] + proto_word_offset; proto_byte = next_table[proto_byte]; Proto = &(ProtoSet->Protos[ProtoNum + proto_offset]); ConfigWord = Proto->Configs[0]; A3 = (((Proto->A * (Feature->X - 128)) << 1) - (Proto->B * (Feature->Y - 128)) + (Proto->C << 9)); M3 = (((inT8) (Feature->Theta - Proto->Angle)) * kIntThetaFudge) << 1; if (A3 < 0) A3 = ~A3; if (M3 < 0) M3 = ~M3; A3 >>= mult_trunc_shift_bits_; M3 >>= mult_trunc_shift_bits_; if (A3 > evidence_mult_mask_) A3 = evidence_mult_mask_; if (M3 > evidence_mult_mask_) M3 = evidence_mult_mask_; A4 = (A3 * A3) + (M3 * M3); A4 >>= table_trunc_shift_bits_; if (A4 > evidence_table_mask_) Evidence = 0; else Evidence = similarity_evidence_table_[A4]; if (PrintFeatureMatchesOn (Debug)) IMDebugConfiguration (FeatureNum, ActualProtoNum + proto_offset, Evidence, ConfigMask, ConfigWord); ConfigWord &= *ConfigMask; UINT8Pointer = tables->feature_evidence_ - 8; config_byte = 0; while (ConfigWord != 0 || config_byte != 0) { while (config_byte == 0) { config_byte = ConfigWord & 0xff; ConfigWord >>= 8; UINT8Pointer += 8; } config_offset = offset_table[config_byte]; config_byte = next_table[config_byte]; if (Evidence > UINT8Pointer[config_offset]) UINT8Pointer[config_offset] = Evidence; } UINT8Pointer = &(tables->proto_evidence_[ActualProtoNum + proto_offset][0]); for (ProtoIndex = ClassTemplate->ProtoLengths[ActualProtoNum + proto_offset]; ProtoIndex > 0; ProtoIndex--, UINT8Pointer++) { if (Evidence > *UINT8Pointer) { Temp = *UINT8Pointer; *UINT8Pointer = Evidence; Evidence = Temp; } else if (Evidence == 0) break; } } } } } if (PrintFeatureMatchesOn(Debug)) { IMDebugConfigurationSum(FeatureNum, tables->feature_evidence_, ClassTemplate->NumConfigs); } IntPointer = tables->sum_feature_evidence_; UINT8Pointer = tables->feature_evidence_; int SumOverConfigs = 0; for (ConfigNum = ClassTemplate->NumConfigs; ConfigNum > 0; ConfigNum--) { int evidence = *UINT8Pointer++; SumOverConfigs += evidence; *IntPointer++ += evidence; } return SumOverConfigs; } /** * Print debugging information for Configuations * @return none * @note Exceptions: none * @note History: Wed Feb 27 14:12:28 MST 1991, RWM, Created. */ #ifndef GRAPHICS_DISABLED void IntegerMatcher::DebugFeatureProtoError( INT_CLASS ClassTemplate, BIT_VECTOR ProtoMask, BIT_VECTOR ConfigMask, const ScratchEvidence& tables, inT16 NumFeatures, int Debug) { FLOAT32 ProtoConfigs[MAX_NUM_CONFIGS]; int ConfigNum; uinT32 ConfigWord; int ProtoSetIndex; uinT16 ProtoNum; uinT8 ProtoWordNum; PROTO_SET ProtoSet; uinT16 ActualProtoNum; if (PrintMatchSummaryOn(Debug)) { cprintf("Configuration Mask:\n"); for (ConfigNum = 0; ConfigNum < ClassTemplate->NumConfigs; ConfigNum++) cprintf("%1d", (((*ConfigMask) >> ConfigNum) & 1)); cprintf("\n"); cprintf("Feature Error for Configurations:\n"); for (ConfigNum = 0; ConfigNum < ClassTemplate->NumConfigs; ConfigNum++) { cprintf( " %5.1f", 100.0 * (1.0 - (FLOAT32) tables.sum_feature_evidence_[ConfigNum] / NumFeatures / 256.0)); } cprintf("\n\n\n"); } if (PrintMatchSummaryOn (Debug)) { cprintf ("Proto Mask:\n"); for (ProtoSetIndex = 0; ProtoSetIndex < ClassTemplate->NumProtoSets; ProtoSetIndex++) { ActualProtoNum = (ProtoSetIndex * PROTOS_PER_PROTO_SET); for (ProtoWordNum = 0; ProtoWordNum < 2; ProtoWordNum++, ProtoMask++) { ActualProtoNum = (ProtoSetIndex * PROTOS_PER_PROTO_SET); for (ProtoNum = 0; ((ProtoNum < (PROTOS_PER_PROTO_SET >> 1)) && (ActualProtoNum < ClassTemplate->NumProtos)); ProtoNum++, ActualProtoNum++) cprintf ("%1d", (((*ProtoMask) >> ProtoNum) & 1)); cprintf ("\n"); } } cprintf ("\n"); } for (int i = 0; i < ClassTemplate->NumConfigs; i++) ProtoConfigs[i] = 0; if (PrintProtoMatchesOn (Debug)) { cprintf ("Proto Evidence:\n"); for (ProtoSetIndex = 0; ProtoSetIndex < ClassTemplate->NumProtoSets; ProtoSetIndex++) { ProtoSet = ClassTemplate->ProtoSets[ProtoSetIndex]; ActualProtoNum = (ProtoSetIndex * PROTOS_PER_PROTO_SET); for (ProtoNum = 0; ((ProtoNum < PROTOS_PER_PROTO_SET) && (ActualProtoNum < ClassTemplate->NumProtos)); ProtoNum++, ActualProtoNum++) { cprintf ("P %3d =", ActualProtoNum); int temp = 0; for (int j = 0; j < ClassTemplate->ProtoLengths[ActualProtoNum]; j++) { uinT8 data = tables.proto_evidence_[ActualProtoNum][j]; cprintf(" %d", data); temp += data; } cprintf(" = %6.4f%%\n", temp / 256.0 / ClassTemplate->ProtoLengths[ActualProtoNum]); ConfigWord = ProtoSet->Protos[ProtoNum].Configs[0]; ConfigNum = 0; while (ConfigWord) { cprintf ("%5d", ConfigWord & 1 ? temp : 0); if (ConfigWord & 1) ProtoConfigs[ConfigNum] += temp; ConfigNum++; ConfigWord >>= 1; } cprintf("\n"); } } } if (PrintMatchSummaryOn (Debug)) { cprintf ("Proto Error for Configurations:\n"); for (ConfigNum = 0; ConfigNum < ClassTemplate->NumConfigs; ConfigNum++) cprintf (" %5.1f", 100.0 * (1.0 - ProtoConfigs[ConfigNum] / ClassTemplate->ConfigLengths[ConfigNum] / 256.0)); cprintf ("\n\n"); } if (PrintProtoMatchesOn (Debug)) { cprintf ("Proto Sum for Configurations:\n"); for (ConfigNum = 0; ConfigNum < ClassTemplate->NumConfigs; ConfigNum++) cprintf (" %4.1f", ProtoConfigs[ConfigNum] / 256.0); cprintf ("\n\n"); cprintf ("Proto Length for Configurations:\n"); for (ConfigNum = 0; ConfigNum < ClassTemplate->NumConfigs; ConfigNum++) cprintf (" %4.1f", (float) ClassTemplate->ConfigLengths[ConfigNum]); cprintf ("\n\n"); } } void IntegerMatcher::DisplayProtoDebugInfo( INT_CLASS ClassTemplate, BIT_VECTOR ProtoMask, BIT_VECTOR ConfigMask, const ScratchEvidence& tables, bool SeparateDebugWindows) { uinT16 ProtoNum; uinT16 ActualProtoNum; PROTO_SET ProtoSet; int ProtoSetIndex; InitIntMatchWindowIfReqd(); if (SeparateDebugWindows) { InitFeatureDisplayWindowIfReqd(); InitProtoDisplayWindowIfReqd(); } for (ProtoSetIndex = 0; ProtoSetIndex < ClassTemplate->NumProtoSets; ProtoSetIndex++) { ProtoSet = ClassTemplate->ProtoSets[ProtoSetIndex]; ActualProtoNum = ProtoSetIndex * PROTOS_PER_PROTO_SET; for (ProtoNum = 0; ((ProtoNum < PROTOS_PER_PROTO_SET) && (ActualProtoNum < ClassTemplate->NumProtos)); ProtoNum++, ActualProtoNum++) { /* Compute Average for Actual Proto */ int temp = 0; for (int i = 0; i < ClassTemplate->ProtoLengths[ActualProtoNum]; i++) temp += tables.proto_evidence_[ActualProtoNum][i]; temp /= ClassTemplate->ProtoLengths[ActualProtoNum]; if ((ProtoSet->Protos[ProtoNum]).Configs[0] & (*ConfigMask)) { DisplayIntProto(ClassTemplate, ActualProtoNum, temp / 255.0); } } } } void IntegerMatcher::DisplayFeatureDebugInfo( INT_CLASS ClassTemplate, BIT_VECTOR ProtoMask, BIT_VECTOR ConfigMask, inT16 NumFeatures, const INT_FEATURE_STRUCT* Features, int AdaptFeatureThreshold, int Debug, bool SeparateDebugWindows) { ScratchEvidence *tables = new ScratchEvidence(); tables->Clear(ClassTemplate); InitIntMatchWindowIfReqd(); if (SeparateDebugWindows) { InitFeatureDisplayWindowIfReqd(); InitProtoDisplayWindowIfReqd(); } for (int Feature = 0; Feature < NumFeatures; Feature++) { UpdateTablesForFeature( ClassTemplate, ProtoMask, ConfigMask, Feature, &Features[Feature], tables, 0); /* Find Best Evidence for Current Feature */ int best = 0; for (int i = 0; i < ClassTemplate->NumConfigs; i++) if (tables->feature_evidence_[i] > best) best = tables->feature_evidence_[i]; /* Update display for current feature */ if (ClipMatchEvidenceOn(Debug)) { if (best < AdaptFeatureThreshold) DisplayIntFeature(&Features[Feature], 0.0); else DisplayIntFeature(&Features[Feature], 1.0); } else { DisplayIntFeature(&Features[Feature], best / 255.0); } } delete tables; } #endif /** * Add sum of Proto Evidences into Sum Of Feature Evidence Array */ void ScratchEvidence::UpdateSumOfProtoEvidences( INT_CLASS ClassTemplate, BIT_VECTOR ConfigMask, inT16 NumFeatures) { int *IntPointer; uinT32 ConfigWord; int ProtoSetIndex; uinT16 ProtoNum; PROTO_SET ProtoSet; int NumProtos; uinT16 ActualProtoNum; NumProtos = ClassTemplate->NumProtos; for (ProtoSetIndex = 0; ProtoSetIndex < ClassTemplate->NumProtoSets; ProtoSetIndex++) { ProtoSet = ClassTemplate->ProtoSets[ProtoSetIndex]; ActualProtoNum = (ProtoSetIndex * PROTOS_PER_PROTO_SET); for (ProtoNum = 0; ((ProtoNum < PROTOS_PER_PROTO_SET) && (ActualProtoNum < NumProtos)); ProtoNum++, ActualProtoNum++) { int temp = 0; for (int i = 0; i < ClassTemplate->ProtoLengths[ActualProtoNum]; i++) temp += proto_evidence_[ActualProtoNum] [i]; ConfigWord = ProtoSet->Protos[ProtoNum].Configs[0]; ConfigWord &= *ConfigMask; IntPointer = sum_feature_evidence_; while (ConfigWord) { if (ConfigWord & 1) *IntPointer += temp; IntPointer++; ConfigWord >>= 1; } } } } /** * Normalize Sum of Proto and Feature Evidence by dividing by the sum of * the Feature Lengths and the Proto Lengths for each configuration. */ void ScratchEvidence::NormalizeSums( INT_CLASS ClassTemplate, inT16 NumFeatures, inT32 used_features) { for (int i = 0; i < ClassTemplate->NumConfigs; i++) { sum_feature_evidence_[i] = (sum_feature_evidence_[i] << 8) / (NumFeatures + ClassTemplate->ConfigLengths[i]); } } /** * Find the best match for the current class and update the Result * with the configuration and match rating. * @return The best normalized sum of evidences * @note Exceptions: none * @note History: Wed Feb 27 14:12:28 MST 1991, RWM, Created. */ int IntegerMatcher::FindBestMatch( INT_CLASS class_template, const ScratchEvidence &tables, UnicharRating* result) { int best_match = 0; result->config = 0; result->fonts.truncate(0); result->fonts.reserve(class_template->NumConfigs); /* Find best match */ for (int c = 0; c < class_template->NumConfigs; ++c) { int rating = tables.sum_feature_evidence_[c]; if (*classify_debug_level_ > 2) tprintf("Config %d, rating=%d\n", c, rating); if (rating > best_match) { result->config = c; best_match = rating; } result->fonts.push_back(ScoredFont(c, rating)); } // Compute confidence on a Probability scale. result->rating = best_match / 65536.0f; return best_match; } /** * Applies the CN normalization factor to the given rating and returns * the modified rating. */ float IntegerMatcher::ApplyCNCorrection(float rating, int blob_length, int normalization_factor, int matcher_multiplier) { return (rating * blob_length + matcher_multiplier * normalization_factor / 256.0) / (blob_length + matcher_multiplier); } /** * Sort Key array in ascending order using heap sort * algorithm. Also sort Index array that is tied to * the key array. * @param n Number of elements to sort * @param ra Key array [1..n] * @param rb Index array [1..n] * @return none * @note Exceptions: none * @note History: Tue Feb 19 10:24:24 MST 1991, RWM, Created. */ void HeapSort (int n, register int ra[], register int rb[]) { register int i, rra, rrb; int l, j, ir; l = (n >> 1) + 1; ir = n; for (;;) { if (l > 1) { rra = ra[--l]; rrb = rb[l]; } else { rra = ra[ir]; rrb = rb[ir]; ra[ir] = ra[1]; rb[ir] = rb[1]; if (--ir == 1) { ra[1] = rra; rb[1] = rrb; return; } } i = l; j = l << 1; while (j <= ir) { if (j < ir && ra[j] < ra[j + 1]) ++j; if (rra < ra[j]) { ra[i] = ra[j]; rb[i] = rb[j]; j += (i = j); } else j = ir + 1; } ra[i] = rra; rb[i] = rrb; } }