ヒストグラムの比較

目次

• 目標
• 理論
• コード
• 説明
• 結果

前のチュートリアル: ヒストグラムの計算
次のチュートリアル: バックプロジェクション

原著者	Ana Huamán
互換性	OpenCV >= 3.0

目標

このチュートリアルでは、以下の方法を学ぶ:

• 関数 cv::compareHist を使い、2つのヒストグラムが互いにどれだけ一致するかを表す数値的な指標を得る。
• さまざまな尺度 (metric) を使ってヒストグラムを比較する

理論

• 2つのヒストグラム（ \(H_{1}\) と \(H_{2}\) ）を比較するには、まず両ヒストグラムがどれだけ一致するかを表す尺度（ \(d(H_{1}, H_{2})\)）を選ぶ必要がある。
• OpenCV implements the function cv::compareHist to perform a comparison. It also offers 6 different metrics to compute the matching:
  1. Correlation ( cv::HISTCMP_CORREL )

     \[d(H_1,H_2) = \frac{\sum_I (H_1(I) - \bar{H_1}) (H_2(I) - \bar{H_2})}{\sqrt{\sum_I(H_1(I) - \bar{H_1})^2 \sum_I(H_2(I) - \bar{H_2})^2}}\]

     where

     \[\bar{H_k} = \frac{1}{N} \sum _J H_k(J)\]

     and \(N\) is the total number of histogram bins.
  2. Chi-Square ( cv::HISTCMP_CHISQR )

     \[d(H_1,H_2) = \sum _I \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)}\]

  3. Intersection ( cv::HISTCMP_INTERSECT )

     \[d(H_1,H_2) = \sum _I \min (H_1(I), H_2(I))\]

  4. Bhattacharyya distance ( cv::HISTCMP_BHATTACHARYYA )

     \[d(H_1,H_2) = \sqrt{1 - \frac{1}{\sqrt{\bar{H_1} \bar{H_2} N^2}} \sum_I \sqrt{H_1(I) \cdot H_2(I)}}\]

  5. Alternative Chi-Square ( cv::HISTCMP_CHISQR_ALT )

     \[d(H_1,H_2) = 2 * \sum _I \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)+H_2(I)}\]

  6. Kullback-Leibler divergence ( cv::HISTCMP_KL_DIV )

     \[d(H_1,H_2) = \sum _I H_1(I) \log \left(\frac{H_1(I)}{H_2(I)}\right)\]

コード

• What does this program do?
  • ベース画像と、それと比較する2枚のテスト画像を読み込む。
  • ベース画像の下半分にあたる画像を1枚生成する
  • 画像をHSV形式に変換する
  • すべての画像についてH-Sヒストグラムを計算し、比較できるように正規化する。
  • ベース画像のヒストグラムを、2つのテストヒストグラム、ベース画像の下半分のヒストグラム、および同じベース画像のヒストグラムと比較する。
  • 得られた数値的な一致の指標を表示する。

C++

• ダウンロード可能なコード: こちらをクリック
• コードの概観:

   
  #include "opencv2/imgcodecs.hpp"
  #include "opencv2/highgui.hpp"
  #include "opencv2/imgproc.hpp"
  #include <iostream>
   
  using namespace std;
  using namespace cv;
   
  const char* keys =
   "{ help h| | Print help message. }"
   "{ @input1 |Histogram_Comparison_Source_0.jpg | Path to input image 1. }"
   "{ @input2 |Histogram_Comparison_Source_1.jpg | Path to input image 2. }"
   "{ @input3 |Histogram_Comparison_Source_2.jpg | Path to input image 3. }";
   
  int main( int argc, char** argv )
  {
   CommandLineParser parser( argc, argv, keys );
   samples::addSamplesDataSearchSubDirectory( "doc/tutorials/imgproc/histograms/histogram_comparison/images" );
   Mat src_base = imread(samples::findFile( parser.get<String>( "@input1" ) ) );
   Mat src_test1 = imread(samples::findFile( parser.get<String>( "@input2" ) ) );
   Mat src_test2 = imread(samples::findFile( parser.get<String>( "@input3" ) ) );
   if( src_base.empty() || src_test1.empty() || src_test2.empty() )
   {
   cout << "Could not open or find the images!\n" << endl;
   parser.printMessage();
   return -1;
   }
   
   Mat hsv_base, hsv_test1, hsv_test2;
   cvtColor( src_base, hsv_base, COLOR_BGR2HSV );
   cvtColor( src_test1, hsv_test1, COLOR_BGR2HSV );
   cvtColor( src_test2, hsv_test2, COLOR_BGR2HSV );
   
   Mat hsv_half_down = hsv_base( Range( hsv_base.rows/2, hsv_base.rows ), Range( 0, hsv_base.cols ) );
   
   int h_bins = 50, s_bins = 60;
   int histSize[] = { h_bins, s_bins };
   
   // hue varies from 0 to 179, saturation from 0 to 255
   float h_ranges[] = { 0, 180 };
   float s_ranges[] = { 0, 256 };
   
   const float* ranges[] = { h_ranges, s_ranges };
   
   // Use the 0-th and 1-st channels
   int channels[] = { 0, 1 };
   
   Mat hist_base, hist_half_down, hist_test1, hist_test2;
   
   calcHist( &hsv_base, 1, channels, Mat(), hist_base, 2, histSize, ranges, true, false );
   normalize( hist_base, hist_base, 1, 0, NORM_L1, -1, Mat() );
   
   calcHist( &hsv_half_down, 1, channels, Mat(), hist_half_down, 2, histSize, ranges, true, false );
   normalize( hist_half_down, hist_half_down, 1, 0, NORM_L1, -1, Mat() );
   
   calcHist( &hsv_test1, 1, channels, Mat(), hist_test1, 2, histSize, ranges, true, false );
   normalize( hist_test1, hist_test1, 1, 0, NORM_L1, -1, Mat() );
   
   calcHist( &hsv_test2, 1, channels, Mat(), hist_test2, 2, histSize, ranges, true, false );
   normalize( hist_test2, hist_test2, 1, 0, NORM_L1, -1, Mat() );
   
   for( int compare_method = 0; compare_method < 6; compare_method++ )
   {
   double base_base = compareHist( hist_base, hist_base, compare_method );
   double base_half = compareHist( hist_base, hist_half_down, compare_method );
   double base_test1 = compareHist( hist_base, hist_test1, compare_method );
   double base_test2 = compareHist( hist_base, hist_test2, compare_method );
   
   cout << "Method " << compare_method << " Perfect, Base-Half, Base-Test(1), Base-Test(2) : "
   << base_base << " / " << base_half << " / " << base_test1 << " / " << base_test2 << endl;
   }
   
   cout << "Done \n";
   return 0;
  }

Java

• ダウンロード可能なコード: こちらをクリック
• コードの全体像:

  import java.util.Arrays;
  import java.util.List;
   
  import org.opencv.core.Core;
  import org.opencv.core.Mat;
  import org.opencv.core.MatOfFloat;
  import org.opencv.core.MatOfInt;
  import org.opencv.core.Range;
  import org.opencv.imgcodecs.Imgcodecs;
  import org.opencv.imgproc.Imgproc;
   
  class CompareHist {
   public void run(String[] args) {
   if (args.length != 3) {
   System.err.println("You must supply 3 arguments that correspond to the paths to 3 images.");
   System.exit(0);
   }
   Mat srcBase = Imgcodecs.imread(args[0]);
   Mat srcTest1 = Imgcodecs.imread(args[1]);
   Mat srcTest2 = Imgcodecs.imread(args[2]);
   if (srcBase.empty() || srcTest1.empty() || srcTest2.empty()) {
   System.err.println("Cannot read the images");
   System.exit(0);
   }
   
   Mat hsvBase = new Mat(), hsvTest1 = new Mat(), hsvTest2 = new Mat();
   Imgproc.cvtColor( srcBase, hsvBase, Imgproc.COLOR_BGR2HSV );
   Imgproc.cvtColor( srcTest1, hsvTest1, Imgproc.COLOR_BGR2HSV );
   Imgproc.cvtColor( srcTest2, hsvTest2, Imgproc.COLOR_BGR2HSV );
   
   Mat hsvHalfDown = hsvBase.submat( new Range( hsvBase.rows()/2, hsvBase.rows() - 1 ), new Range( 0, hsvBase.cols() - 1 ) );
   
   int hBins = 50, sBins = 60;
   int[] histSize = { hBins, sBins };
   
   // hue varies from 0 to 179, saturation from 0 to 255
   float[] ranges = { 0, 180, 0, 256 };
   
   // Use the 0-th and 1-st channels
   int[] channels = { 0, 1 };
   
   Mat histBase = new Mat(), histHalfDown = new Mat(), histTest1 = new Mat(), histTest2 = new Mat();
   
   List<Mat> hsvBaseList = Arrays.asList(hsvBase);
   Imgproc.calcHist(hsvBaseList, new MatOfInt(channels), new Mat(), histBase, new MatOfInt(histSize), new MatOfFloat(ranges), false);
   Core.normalize(histBase, histBase, 1, 0, Core.NORM_L1);
   
   List<Mat> hsvHalfDownList = Arrays.asList(hsvHalfDown);
   Imgproc.calcHist(hsvHalfDownList, new MatOfInt(channels), new Mat(), histHalfDown, new MatOfInt(histSize), new MatOfFloat(ranges), false);
   Core.normalize(histHalfDown, histHalfDown, 1, 0, Core.NORM_L1);
   
   List<Mat> hsvTest1List = Arrays.asList(hsvTest1);
   Imgproc.calcHist(hsvTest1List, new MatOfInt(channels), new Mat(), histTest1, new MatOfInt(histSize), new MatOfFloat(ranges), false);
   Core.normalize(histTest1, histTest1, 1, 0, Core.NORM_L1);
   
   List<Mat> hsvTest2List = Arrays.asList(hsvTest2);
   Imgproc.calcHist(hsvTest2List, new MatOfInt(channels), new Mat(), histTest2, new MatOfInt(histSize), new MatOfFloat(ranges), false);
   Core.normalize(histTest2, histTest2, 1, 0, Core.NORM_L1);
   
   for( int compareMethod = 0; compareMethod < 6; compareMethod++ ) {
   double baseBase = Imgproc.compareHist( histBase, histBase, compareMethod );
   double baseHalf = Imgproc.compareHist( histBase, histHalfDown, compareMethod );
   double baseTest1 = Imgproc.compareHist( histBase, histTest1, compareMethod );
   double baseTest2 = Imgproc.compareHist( histBase, histTest2, compareMethod );
   
   System.out.println("Method " + compareMethod + " Perfect, Base-Half, Base-Test(1), Base-Test(2) : " + baseBase + " / " + baseHalf
   + " / " + baseTest1 + " / " + baseTest2);
   }
   }
  }
   
  public class CompareHistDemo {
   public static void main(String[] args) {
   // Load the native OpenCV library
   System.loadLibrary(Core.NATIVE_LIBRARY_NAME);
   
   new CompareHist().run(args);
   }
  }

Python

• ダウンロード可能なコード: こちらをクリック
• コード全体:

  from __future__ import print_function
  from __future__ import division
  import cv2 as cv
  import numpy as np
  import argparse
   
   
  parser = argparse.ArgumentParser(description='Code for Histogram Comparison tutorial.')
  parser.add_argument('--input1', help='Path to input image 1.')
  parser.add_argument('--input2', help='Path to input image 2.')
  parser.add_argument('--input3', help='Path to input image 3.')
  args = parser.parse_args()
   
  src_base = cv.imread(args.input1)
  src_test1 = cv.imread(args.input2)
  src_test2 = cv.imread(args.input3)
  if src_base is None or src_test1 is None or src_test2 is None:
   print('Could not open or find the images!')
   exit(0)
   
   
   
  hsv_base = cv.cvtColor(src_base, cv.COLOR_BGR2HSV)
  hsv_test1 = cv.cvtColor(src_test1, cv.COLOR_BGR2HSV)
  hsv_test2 = cv.cvtColor(src_test2, cv.COLOR_BGR2HSV)
   
   
   
  hsv_half_down = hsv_base[hsv_base.shape[0]//2:,:]
   
   
   
  h_bins = 50
  s_bins = 60
  histSize = [h_bins, s_bins]
   
  # hue varies from 0 to 179, saturation from 0 to 255
  h_ranges = [0, 180]
  s_ranges = [0, 256]
  ranges = h_ranges + s_ranges # concat lists
   
  # Use the 0-th and 1-st channels
  channels = [0, 1]
   
   
   
  hist_base = cv.calcHist([hsv_base], channels, None, histSize, ranges, accumulate=False)
  cv.normalize(hist_base, hist_base, alpha=1, beta=0, norm_type=cv.NORM_L1)
   
  hist_half_down = cv.calcHist([hsv_half_down], channels, None, histSize, ranges, accumulate=False)
  cv.normalize(hist_half_down, hist_half_down, alpha=1, beta=0, norm_type=cv.NORM_L1)
   
  hist_test1 = cv.calcHist([hsv_test1], channels, None, histSize, ranges, accumulate=False)
  cv.normalize(hist_test1, hist_test1, alpha=1, beta=0, norm_type=cv.NORM_L1)
   
  hist_test2 = cv.calcHist([hsv_test2], channels, None, histSize, ranges, accumulate=False)
  cv.normalize(hist_test2, hist_test2, alpha=1, beta=0, norm_type=cv.NORM_L1)
   
   
   
  for compare_method in range(6):
   base_base = cv.compareHist(hist_base, hist_base, compare_method)
   base_half = cv.compareHist(hist_base, hist_half_down, compare_method)
   base_test1 = cv.compareHist(hist_base, hist_test1, compare_method)
   base_test2 = cv.compareHist(hist_base, hist_test2, compare_method)
   
   print('Method:', compare_method, 'Perfect, Base-Half, Base-Test(1), Base-Test(2) :',\
   base_base, '/', base_half, '/', base_test1, '/', base_test2)
   

解説

• ベース画像 (src_base) と他の2枚のテスト画像を読み込む:

  C++

   CommandLineParser parser( argc, argv, keys );
      samples::addSamplesDataSearchSubDirectory( "doc/tutorials/imgproc/histograms/histogram_comparison/images" );
   Mat src_base = imread(samples::findFile( parser.get<String>( "@input1" ) ) );
   Mat src_test1 = imread(samples::findFile( parser.get<String>( "@input2" ) ) );
   Mat src_test2 = imread(samples::findFile( parser.get<String>( "@input3" ) ) );
   if( src_base.empty() || src_test1.empty() || src_test2.empty() )
      {
          cout << "Could not open or find the images!\n" << endl;
          parser.printMessage();
   return -1;
      }

  Java

   if (args.length != 3) {
              System.err.println("You must supply 3 arguments that correspond to the paths to 3 images.");
              System.exit(0);
          }
          Mat srcBase = Imgcodecs.imread(args[0]);
          Mat srcTest1 = Imgcodecs.imread(args[1]);
          Mat srcTest2 = Imgcodecs.imread(args[2]);
   if (srcBase.empty() || srcTest1.empty() || srcTest2.empty()) {
              System.err.println("Cannot read the images");
              System.exit(0);
          }

  Python

  parser = argparse.ArgumentParser(description='Code for Histogram Comparison tutorial.')
  parser.add_argument('--input1', help='Path to input image 1.')
  parser.add_argument('--input2', help='Path to input image 2.')
  parser.add_argument('--input3', help='Path to input image 3.')
  args = parser.parse_args()
   
  src_base = cv.imread(args.input1)
  src_test1 = cv.imread(args.input2)
  src_test2 = cv.imread(args.input3)
  if src_base is None or src_test1 is None or src_test2 is None:
      print('Could not open or find the images!')
      exit(0)

• それらをHSV形式に変換する:

  C++

   Mat hsv_base, hsv_test1, hsv_test2;
   cvtColor( src_base, hsv_base, COLOR_BGR2HSV );
   cvtColor( src_test1, hsv_test1, COLOR_BGR2HSV );
   cvtColor( src_test2, hsv_test2, COLOR_BGR2HSV );

  Java

          Mat hsvBase = new Mat(), hsvTest1 = new Mat(), hsvTest2 = new Mat();
          Imgproc.cvtColor( srcBase, hsvBase, Imgproc.COLOR_BGR2HSV );
          Imgproc.cvtColor( srcTest1, hsvTest1, Imgproc.COLOR_BGR2HSV );
          Imgproc.cvtColor( srcTest2, hsvTest2, Imgproc.COLOR_BGR2HSV );

  Python

  hsv_base = cv.cvtColor(src_base, cv.COLOR_BGR2HSV)
  hsv_test1 = cv.cvtColor(src_test1, cv.COLOR_BGR2HSV)
  hsv_test2 = cv.cvtColor(src_test2, cv.COLOR_BGR2HSV)

• さらに、ベース画像の半分のサイズの画像を作成する (HSV形式):

  C++

   Mat hsv_half_down = hsv_base( Range( hsv_base.rows/2, hsv_base.rows ), Range( 0, hsv_base.cols ) );

  Java

          Mat hsvHalfDown = hsvBase.submat( new Range( hsvBase.rows()/2, hsvBase.rows() - 1 ), new Range( 0, hsvBase.cols() - 1 ) );

  Python

  hsv_half_down = hsv_base[hsv_base.shape[0]//2:,:]

• ヒストグラムを計算するための引数 (bins、ranges、チャンネルHおよびS) を初期化する。

  C++

   int h_bins = 50, s_bins = 60;
   int histSize[] = { h_bins, s_bins };
   
   // hue varies from 0 to 179, saturation from 0 to 255
   float h_ranges[] = { 0, 180 };
   float s_ranges[] = { 0, 256 };
   
   const float* ranges[] = { h_ranges, s_ranges };
   
   // Use the 0-th and 1-st channels
   int channels[] = { 0, 1 };

  Java

   int hBins = 50, sBins = 60;
   int[] histSize = { hBins, sBins };
   
   // hue varies from 0 to 179, saturation from 0 to 255
   float[] ranges = { 0, 180, 0, 256 };
   
   // Use the 0-th and 1-st channels
   int[] channels = { 0, 1 };

  Python

  h_bins = 50
  s_bins = 60
  histSize = [h_bins, s_bins]
   
  # hue varies from 0 to 179, saturation from 0 to 255
  h_ranges = [0, 180]
  s_ranges = [0, 256]
  ranges = h_ranges + s_ranges # concat lists
   
  # Use the 0-th and 1-st channels
  channels = [0, 1]

• ベース画像、2枚のテスト画像、および下半分のベース画像についてヒストグラムを計算する:

  C++

   Mat hist_base, hist_half_down, hist_test1, hist_test2;
   
   calcHist( &hsv_base, 1, channels, Mat(), hist_base, 2, histSize, ranges, true, false );
   normalize( hist_base, hist_base, 1, 0, NORM_L1, -1, Mat() );
   
   calcHist( &hsv_half_down, 1, channels, Mat(), hist_half_down, 2, histSize, ranges, true, false );
   normalize( hist_half_down, hist_half_down, 1, 0, NORM_L1, -1, Mat() );
   
   calcHist( &hsv_test1, 1, channels, Mat(), hist_test1, 2, histSize, ranges, true, false );
   normalize( hist_test1, hist_test1, 1, 0, NORM_L1, -1, Mat() );
   
   calcHist( &hsv_test2, 1, channels, Mat(), hist_test2, 2, histSize, ranges, true, false );
   normalize( hist_test2, hist_test2, 1, 0, NORM_L1, -1, Mat() );

  Java

          Mat histBase = new Mat(), histHalfDown = new Mat(), histTest1 = new Mat(), histTest2 = new Mat();
   
          List<Mat> hsvBaseList = Arrays.asList(hsvBase);
          Imgproc.calcHist(hsvBaseList, new MatOfInt(channels), new Mat(), histBase, new MatOfInt(histSize), new MatOfFloat(ranges), false);
          Core.normalize(histBase, histBase, 1, 0, Core.NORM_L1);
   
          List<Mat> hsvHalfDownList = Arrays.asList(hsvHalfDown);
          Imgproc.calcHist(hsvHalfDownList, new MatOfInt(channels), new Mat(), histHalfDown, new MatOfInt(histSize), new MatOfFloat(ranges), false);
          Core.normalize(histHalfDown, histHalfDown, 1, 0, Core.NORM_L1);
   
          List<Mat> hsvTest1List = Arrays.asList(hsvTest1);
          Imgproc.calcHist(hsvTest1List, new MatOfInt(channels), new Mat(), histTest1, new MatOfInt(histSize), new MatOfFloat(ranges), false);
          Core.normalize(histTest1, histTest1, 1, 0, Core.NORM_L1);
   
          List<Mat> hsvTest2List = Arrays.asList(hsvTest2);
          Imgproc.calcHist(hsvTest2List, new MatOfInt(channels), new Mat(), histTest2, new MatOfInt(histSize), new MatOfFloat(ranges), false);
          Core.normalize(histTest2, histTest2, 1, 0, Core.NORM_L1);

  Python

  hist_base = cv.calcHist([hsv_base], channels, None, histSize, ranges, accumulate=False)
  cv.normalize(hist_base, hist_base, alpha=1, beta=0, norm_type=cv.NORM_L1)
   
  hist_half_down = cv.calcHist([hsv_half_down], channels, None, histSize, ranges, accumulate=False)
  cv.normalize(hist_half_down, hist_half_down, alpha=1, beta=0, norm_type=cv.NORM_L1)
   
  hist_test1 = cv.calcHist([hsv_test1], channels, None, histSize, ranges, accumulate=False)
  cv.normalize(hist_test1, hist_test1, alpha=1, beta=0, norm_type=cv.NORM_L1)
   
  hist_test2 = cv.calcHist([hsv_test2], channels, None, histSize, ranges, accumulate=False)
  cv.normalize(hist_test2, hist_test2, alpha=1, beta=0, norm_type=cv.NORM_L1)

• ベース画像のヒストグラム (hist_base) と他のヒストグラムとの間で、6種類の比較手法を順に適用する:

  C++

   for( int compare_method = 0; compare_method < 6; compare_method++ )
      {
   double base_base = compareHist( hist_base, hist_base, compare_method );
   double base_half = compareHist( hist_base, hist_half_down, compare_method );
   double base_test1 = compareHist( hist_base, hist_test1, compare_method );
   double base_test2 = compareHist( hist_base, hist_test2, compare_method );
   
          cout << "Method " << compare_method << " Perfect, Base-Half, Base-Test(1), Base-Test(2) : "
               <<  base_base << " / " << base_half << " / " << base_test1 << " / " << base_test2 << endl;
      }

  Java

   for( int compareMethod = 0; compareMethod < 6; compareMethod++ ) {
   double baseBase = Imgproc.compareHist( histBase, histBase, compareMethod );
   double baseHalf = Imgproc.compareHist( histBase, histHalfDown, compareMethod );
   double baseTest1 = Imgproc.compareHist( histBase, histTest1, compareMethod );
   double baseTest2 = Imgproc.compareHist( histBase, histTest2, compareMethod );
   
              System.out.println("Method " + compareMethod + " Perfect, Base-Half, Base-Test(1), Base-Test(2) : " + baseBase + " / " + baseHalf
                      + " / " + baseTest1 + " / " + baseTest2);
          }

  Python

  for compare_method in range(6):
      base_base = cv.compareHist(hist_base, hist_base, compare_method)
      base_half = cv.compareHist(hist_base, hist_half_down, compare_method)
      base_test1 = cv.compareHist(hist_base, hist_test1, compare_method)
      base_test2 = cv.compareHist(hist_base, hist_test2, compare_method)
   
      print('Method:', compare_method, 'Perfect, Base-Half, Base-Test(1), Base-Test(2) :',\
            base_base, '/', base_half, '/', base_test1, '/', base_test2)

結果

1. 入力として以下の画像を使用する:

最初の画像がベース (他と比較される対象) で、残りの2枚がテスト画像である。さらに、最初の画像をそれ自身と比較し、またベース画像の半分と比較する。

1. ベース画像のヒストグラムをそれ自身と比較した場合は、完全に一致することが期待される。また、ベース画像の半分のヒストグラムと比較した場合も、両者は同じソース由来であるため高い一致度を示すはずである。他の2枚のテスト画像については、照明条件が大きく異なるため、一致度はあまり良くならないはずである:

2. OpenCV 4.12.0 で得られた数値結果を以下に示す:

   手法	Base - Base	Base - Half	Base - Test 1	Base - Test 2
   Correlation	1.000000	0.880438	0.20457	0.065752
   Chi-square	0.000000	0.328307	181.674	80.1494
   Intersection	1.000000	0.75005	0.315061	0.0908022
   Bhattacharyya	0.000000	0.237866	0.679825	0.873709
   Chi-Square alt.	0.000000	0.395046	2.31572	3.41024
   KL divergence	0.000000	0.321064	2.6616	9.55412

   Correlation および Intersection の手法では、指標が大きいほど一致が正確である。見ての通り、base-base の一致が予想通り最も高い。また、base-half の一致が (予測した通り) 2番目に良い一致であることがわかる。残りの4つの指標では、結果が小さいほど一致が良い。