3.4直方圖對比
3.4.1直方圖對比概述
要比較兩個直方圖( and ), 首先必須要選擇一個衡量直方圖相似度的對比标準 。OpenCV 函數 compareHist 執行了具體的直方圖對比的任務。該函數提供了4種對比标準來計算相似度：
相關：Correlation ( CV_COMP_CORREL )
其中
是直方圖中bin的數目。
卡方：Chi-Square ( CV_COMP_CHISQR )
直方圖相交：Intersection ( CV_COMP_INTERSECT )
Bhattacharyya 距離( CV_COMP_BHATTACHARYYA )
3.4.2直方圖對比相關API及源碼
compareHist()函數原型
C++: double compareHist(InputArray H1,
InputArray H2,
int method) C++: double compareHist(const SparseMat& H1,
const SparseMat& H2,
int method) 【參數】
第一個參數，H1 – First compared histogram.
第二個參數，H2 – Second compared histogram of the same size as H1 .
第三個參數，method -Comparison method that could be one of the following:
CV_COMP_CORREL Correlation
CV_COMP_CHISQR Chi-Square
CV_COMP_INTERSECT Intersection
CV_COMP_BHATTACHARYYA Bhattacharyya distance
compareHist()函數源代碼
/*【compareHist ( )源代碼】***********************************************************
* @Version：OpenCV 3.0.0（Opnencv2和Opnencv3差别不大，Linux和PC的對應版本源碼完全一樣，均在對應的安裝目錄下）
* @源碼路徑：…\opencv\sources\modules\imgproc\src\histogram.cpp
* @起始行數：2272行
********************************************************************************/
double cv::compareHist( InputArray _H1, InputArray _H2, int method )
{
Mat H1 = _H1.getMat(), H2 = _H2.getMat();
const Mat* arrays[] = {&H1, &H2, 0};
Mat planes[2];
NAryMatIterator it(arrays, planes);
double result = 0;
int j, len = (int)it.size;
CV_Assert( H1.type() == H2.type() && H1.depth() == CV_32F );
double s1 = 0, s2 = 0, s11 = 0, s12 = 0, s22 = 0;
CV_Assert( it.planes[0].isContinuous() && it.planes[1].isContinuous() );
#if CV_SSE2
bool haveSIMD = checkHardwareSupport(CV_CPU_SSE2);
#endif
for( size_t i = 0; i < it.nplanes; i++, ++it )
{
const float* h1 = it.planes[0].ptr<float>();
const float* h2 = it.planes[1].ptr<float>();
len = it.planes[0].rows*it.planes[0].cols*H1.channels();
j = 0;
if( (method == CV_COMP_CHISQR) || (method == CV_COMP_CHISQR_ALT))
{
for( ; j < len; j++ )
{
double a = h1[j] - h2[j];
double b = (method == CV_COMP_CHISQR) ? h1[j] : h1[j] + h2[j];
if( fabs(b) > DBL_EPSILON )
result += a*a/b;
}
}
else if( method == CV_COMP_CORREL )
{
#if CV_SSE2
if (haveSIMD)
{
__m128d v_s1 = _mm_setzero_pd(), v_s2 = v_s1;
__m128d v_s11 = v_s1, v_s22 = v_s1, v_s12 = v_s1;
for ( ; j <= len - 4; j += 4)
{
__m128 v_a = _mm_loadu_ps(h1 + j);
__m128 v_b = _mm_loadu_ps(h2 + j);
// 0-1
__m128d v_ad = _mm_cvtps_pd(v_a);
__m128d v_bd = _mm_cvtps_pd(v_b);
v_s12 = _mm_add_pd(v_s12, _mm_mul_pd(v_ad, v_bd));
v_s11 = _mm_add_pd(v_s11, _mm_mul_pd(v_ad, v_ad));
v_s22 = _mm_add_pd(v_s22, _mm_mul_pd(v_bd, v_bd));
v_s1 = _mm_add_pd(v_s1, v_ad);
v_s2 = _mm_add_pd(v_s2, v_bd);
// 2-3
v_ad = _mm_cvtps_pd(_mm_castsi128_ps(_mm_srli_si128(_mm_castps_si128(v_a), 8)));
v_bd = _mm_cvtps_pd(_mm_castsi128_ps(_mm_srli_si128(_mm_castps_si128(v_b), 8)));
v_s12 = _mm_add_pd(v_s12, _mm_mul_pd(v_ad, v_bd));
v_s11 = _mm_add_pd(v_s11, _mm_mul_pd(v_ad, v_ad));
v_s22 = _mm_add_pd(v_s22, _mm_mul_pd(v_bd, v_bd));
v_s1 = _mm_add_pd(v_s1, v_ad);
v_s2 = _mm_add_pd(v_s2, v_bd);
}
double CV_DECL_ALIGNED(16) ar[10];
_mm_store_pd(ar, v_s12);
_mm_store_pd(ar + 2, v_s11);
_mm_store_pd(ar + 4, v_s22);
_mm_store_pd(ar + 6, v_s1);
_mm_store_pd(ar + 8, v_s2);
s12 += ar[0] + ar[1];
s11 += ar[2] + ar[3];
s22 += ar[4] + ar[5];
s1 += ar[6] + ar[7];
s2 += ar[8] + ar[9];
}
#endif
for( ; j < len; j++ )
{
double a = h1[j];
double b = h2[j];
s12 += a*b;
s1 += a;
s11 += a*a;
s2 += b;
s22 += b*b;
}
}
else if( method == CV_COMP_INTERSECT )
{
#if CV_NEON
float32x4_t v_result = vdupq_n_f32(0.0f);
for( ; j <= len - 4; j += 4 )
v_result = vaddq_f32(v_result, vminq_f32(vld1q_f32(h1 + j), vld1q_f32(h2 + j)));
float CV_DECL_ALIGNED(16) ar[4];
vst1q_f32(ar, v_result);
result += ar[0] + ar[1] + ar[2] + ar[3];
#elif CV_SSE2
if (haveSIMD)
{
__m128d v_result = _mm_setzero_pd();
for ( ; j <= len - 4; j += 4)
{
__m128 v_src = _mm_min_ps(_mm_loadu_ps(h1 + j),
_mm_loadu_ps(h2 + j));
v_result = _mm_add_pd(v_result, _mm_cvtps_pd(v_src));
v_src = _mm_castsi128_ps(_mm_srli_si128(_mm_castps_si128(v_src), 8));
v_result = _mm_add_pd(v_result, _mm_cvtps_pd(v_src));
}
double CV_DECL_ALIGNED(16) ar[2];
_mm_store_pd(ar, v_result);
result += ar[0] + ar[1];
}
#endif
for( ; j < len; j++ )
result += std::min(h1[j], h2[j]);
}
else if( method == CV_COMP_BHATTACHARYYA )
{
#if CV_SSE2
if (haveSIMD)
{
__m128d v_s1 = _mm_setzero_pd(), v_s2 = v_s1, v_result = v_s1;
for ( ; j <= len - 4; j += 4)
{
__m128 v_a = _mm_loadu_ps(h1 + j);
__m128 v_b = _mm_loadu_ps(h2 + j);
__m128d v_ad = _mm_cvtps_pd(v_a);
__m128d v_bd = _mm_cvtps_pd(v_b);
v_s1 = _mm_add_pd(v_s1, v_ad);
v_s2 = _mm_add_pd(v_s2, v_bd);
v_result = _mm_add_pd(v_result, _mm_sqrt_pd(_mm_mul_pd(v_ad, v_bd)));
v_ad = _mm_cvtps_pd(_mm_castsi128_ps(_mm_srli_si128(_mm_castps_si128(v_a), 8)));
v_bd = _mm_cvtps_pd(_mm_castsi128_ps(_mm_srli_si128(_mm_castps_si128(v_b), 8)));
v_s1 = _mm_add_pd(v_s1, v_ad);
v_s2 = _mm_add_pd(v_s2, v_bd);
v_result = _mm_add_pd(v_result, _mm_sqrt_pd(_mm_mul_pd(v_ad, v_bd)));
}
double CV_DECL_ALIGNED(16) ar[6];
_mm_store_pd(ar, v_s1);
_mm_store_pd(ar + 2, v_s2);
_mm_store_pd(ar + 4, v_result);
s1 += ar[0] + ar[1];
s2 += ar[2] + ar[3];
result += ar[4] + ar[5];
}
#endif
for( ; j < len; j++ )
{
double a = h1[j];
double b = h2[j];
result += std::sqrt(a*b);
s1 += a;
s2 += b;
}
}
else if( method == CV_COMP_KL_DIV )
{
for( ; j < len; j++ )
{
double p = h1[j];
double q = h2[j];
if( fabs(p) <= DBL_EPSILON ) {
continue;
}
if( fabs(q) <= DBL_EPSILON ) {
q = 1e-10;
}
result += p * std::log( p / q );
}
}
else
CV_Error( CV_StsBadArg, "Unknown comparison method" );
}
if( method == CV_COMP_CHISQR_ALT )
result *= 2;
else if( method == CV_COMP_CORREL )
{
size_t total = H1.total();
double scale = 1./total;
double num = s12 - s1*s2*scale;
double denom2 = (s11 - s1*s1*scale)*(s22 - s2*s2*scale);
result = std::abs(denom2) > DBL_EPSILON ? num/std::sqrt(denom2) : 1.;
}
else if( method == CV_COMP_BHATTACHARYYA )
{
s1 *= s2;
s1 = fabs(s1) > FLT_EPSILON ? 1./std::sqrt(s1) : 1.;
result = std::sqrt(std::max(1. - result*s1, 0.));
}
return result;
} /*【compareHist ( )源代碼】***********************************************************
* @Version：OpenCV 3.0.0（Opnencv2和Opnencv3差别不大，Linux和PC的對應版本源碼完全一樣，均在對應的安裝目錄下）
* @源碼路徑：…\opencv\sources\modules\imgproc\src\histogram.cpp
* @起始行數： 2478行
********************************************************************************/
double cv::compareHist( const SparseMat& H1, const SparseMat& H2, int method )
{
double result = 0;
int i, dims = H1.dims();
CV_Assert( dims > 0 && dims == H2.dims() && H1.type() == H2.type() && H1.type() == CV_32F );
for( i = 0; i < dims; i++ )
CV_Assert( H1.size(i) == H2.size(i) );
const SparseMat *PH1 = &H1, *PH2 = &H2;
if( PH1->nzcount() > PH2->nzcount() && method != CV_COMP_CHISQR && method != CV_COMP_CHISQR_ALT && method != CV_COMP_KL_DIV )
std::swap(PH1, PH2);
SparseMatConstIterator it = PH1->begin();
int N1 = (int)PH1->nzcount(), N2 = (int)PH2->nzcount();
if( (method == CV_COMP_CHISQR) || (method == CV_COMP_CHISQR_ALT) )
{
for( i = 0; i < N1; i++, ++it )
{
float v1 = it.value<float>();
const SparseMat::Node* node = it.node();
float v2 = PH2->value<float>(node->idx, (size_t*)&node->hashval);
double a = v1 - v2;
double b = (method == CV_COMP_CHISQR) ? v1 : v1 + v2;
if( fabs(b) > DBL_EPSILON )
result += a*a/b;
}
}
else if( method == CV_COMP_CORREL )
{
double s1 = 0, s2 = 0, s11 = 0, s12 = 0, s22 = 0;
for( i = 0; i < N1; i++, ++it )
{
double v1 = it.value<float>();
const SparseMat::Node* node = it.node();
s12 += v1*PH2->value<float>(node->idx, (size_t*)&node->hashval);
s1 += v1;
s11 += v1*v1;
}
it = PH2->begin();
for( i = 0; i < N2; i++, ++it )
{
double v2 = it.value<float>();
s2 += v2;
s22 += v2*v2;
}
size_t total = 1;
for( i = 0; i < H1.dims(); i++ )
total *= H1.size(i);
double scale = 1./total;
double num = s12 - s1*s2*scale;
double denom2 = (s11 - s1*s1*scale)*(s22 - s2*s2*scale);
result = std::abs(denom2) > DBL_EPSILON ? num/std::sqrt(denom2) : 1.;
}
else if( method == CV_COMP_INTERSECT )
{
for( i = 0; i < N1; i++, ++it )
{
float v1 = it.value<float>();
const SparseMat::Node* node = it.node();
float v2 = PH2->value<float>(node->idx, (size_t*)&node->hashval);
if( v2 )
result += std::min(v1, v2);
}
}
else if( method == CV_COMP_BHATTACHARYYA )
{
double s1 = 0, s2 = 0;
for( i = 0; i < N1; i++, ++it )
{
double v1 = it.value<float>();
const SparseMat::Node* node = it.node();
double v2 = PH2->value<float>(node->idx, (size_t*)&node->hashval);
result += std::sqrt(v1*v2);
s1 += v1;
}
it = PH2->begin();
for( i = 0; i < N2; i++, ++it )
s2 += it.value<float>();
s1 *= s2;
s1 = fabs(s1) > FLT_EPSILON ? 1./std::sqrt(s1) : 1.;
result = std::sqrt(std::max(1. - result*s1, 0.));
}
else if( method == CV_COMP_KL_DIV )
{
for( i = 0; i < N1; i++, ++it )
{
double v1 = it.value<float>();
const SparseMat::Node* node = it.node();
double v2 = PH2->value<float>(node->idx, (size_t*)&node->hashval);
if( !v2 )
v2 = 1e-10;
result += v1 * std::log( v1 / v2 );
}
}
else
CV_Error( CV_StsBadArg, "Unknown comparison method" );
if( method == CV_COMP_CHISQR_ALT )
result *= 2;
return result;
} 3.4.3直方圖對比執行個體
代碼參看附件【demo1】。
圖1
圖2
圖3