CV中直方图比较方法
为了比较两个直方图 ( H 1 和 H 2 ) (H_{1}和H_{2}) (H1和H2)，首先必须选择度量 ( d ( H 1 H 2 ) ) (d(H_{1}H_{2})) (d(H1H2))，以表示两个直方图匹配的程度。
OpenCV利用函数compareHist来执行比较。它还提供4个不同的度量来计算匹配：
1、皮尔逊相关系数
Correlation ( CV_COMP_CORREL )
d ( H 1 , H 2 ) = ∑ I ( H 1 ( I ) − H 1 ˉ ) ( H 2 ( I ) − H 2 ˉ ) ∑ I ( H 1 ( I ) − H 1 ˉ ) 2 ∑ I ( H 2 ( I ) − H 2 ˉ ) 2 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}} d(H1,H2)=∑I(H1(I)−H1ˉ)2∑I(H2(I)−H2ˉ)2∑I(H1(I)−H1ˉ)(H2(I)−H2ˉ)
其中
H k ˉ = 1 N ∑ J H k ( J ) \bar{H_k} = \frac{1}{N} \sum _J H_k(J) Hkˉ=N1J∑Hk(J)
N是直方图区间总数。
真值 [1.00]
取值区间 [0.00,1.00]
2、卡方距离
Chi-Square ( CV_COMP_CHISQR )
d ( H 1 , H 2 ) = ∑ I ( H 1 ( I ) − H 2 ( I ) ) 2 H 1 ( I ) d(H_1,H_2) = \sum _I \frac{\left(H_1(I)-H_2(I)\right)^2}{H_1(I)} d(H1,H2)=I∑H1(I)(H1(I)−H2(I))2
真值 [0.00]
取值区间 [0.00,+∞]
3、交叉距离
Intersection ( method=CV_COMP_INTERSECT )
d ( H 1 , H 2 ) = ∑ I min ( H 1 ( I ) , H 2 ( I ) ) d(H_1,H_2) = \sum _I \min (H_1(I), H_2(I)) d(H1,H2)=I∑min(H1(I),H2(I))
真值 [24.39]
取值区间 [0.00,1.00]
4、巴氏距离
Bhattacharyya distance ( CV_COMP_BHATTACHARYYA )
d ( H 1 , H 2 ) = 1 − 1 H 1 ˉ H 2 ˉ N 2 ∑ I H 1 ( I ) ⋅ H 2 ( I ) 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)}} d(H1,H2)=1−H1ˉH2ˉN21I∑H1(I)⋅H2(I)
真值 [0.00]
取值区间 [0.00,1.00]
[1]https://docs.opencv.org/2.4/doc/tutorials/imgproc/histograms/histogram_comparison/histogram_comparison.html