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semi_global_matching.cpp
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semi_global_matching.cpp
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#include "semi_global_matching.h"
#include <opencv2/imgproc.hpp>
#define USE_OPENMP
#if defined(_OPENMP) && defined(USE_OPENMP)
#ifdef _WIN32
#define OMP_PARALLEL_FOR __pragma(omp parallel for)
#else
#define OMP_PARALLEL_FOR _Pragma("omp parallel for")
#endif
#else
#define OMP_PARALLEL_FOR
#endif
#ifdef _WIN32
#define popcnt32 __popcnt
#define popcnt64 __popcnt64
#else
#define popcnt32 __builtin_popcount
#define popcnt64 __builtin_popcountll
#endif
#define WITH_SSE
#ifdef WITH_SSE
#include <smmintrin.h>
static inline int _mm_hmin_epu8(__m128i v)
{
v = _mm_min_epu8(v, _mm_shuffle_epi32(v, _MM_SHUFFLE(3, 2, 3, 2)));
v = _mm_min_epu8(v, _mm_shuffle_epi32(v, _MM_SHUFFLE(1, 1, 1, 1)));
v = _mm_min_epu8(v, _mm_shufflelo_epi16(v, _MM_SHUFFLE(1, 1, 1, 1)));
v = _mm_min_epu8(v, _mm_srli_epi16(v, 8));
return static_cast<uchar>(_mm_cvtsi128_si32(v));
}
static inline __m128i _mm_set1_epi_(uint32_t v) { return _mm_set1_epi32(v); }
static inline __m128i _mm_set1_epi_(uint64_t v) { return _mm_set1_epi64x(v); }
#endif
static const int DEFAULT_MC = 64;
static inline int HammingDistance(uint64_t c1, uint64_t c2) { return static_cast<int>(popcnt64(c1 ^ c2)); }
static inline int HammingDistance(uint32_t c1, uint32_t c2) { return static_cast<int>(popcnt32(c1 ^ c2)); }
static inline int min4(int x, int y, int z, int w)
{
return std::min(std::min(x, y), std::min(z, w));
};
template <int VIEW = 0>
static void census9x7(const cv::Mat& src, cv::Mat& dst)
{
CV_Assert(dst.elemSize() == 8);
memset(dst.data, 0, dst.rows * dst.cols * sizeof(uint64_t));
const int RADIUS_U = 9 / 2;
const int RADIUS_V = 7 / 2;
int v;
OMP_PARALLEL_FOR
for (v = RADIUS_V; v < src.rows - RADIUS_V; v++)
{
uint64_t* dstptr = dst.ptr<uint64>(v);
for (int u = RADIUS_U; u < src.cols - RADIUS_U; u++)
{
uint64_t c = 0;
for (int dv = -RADIUS_V; dv <= RADIUS_V; dv++)
{
for (int du = -RADIUS_U; du <= RADIUS_U; du++)
{
c <<= 1;
c += src.ptr(v)[u] <= src.ptr(v + dv)[u + du] ? 0 : 1;
}
}
if (VIEW == 0)
dstptr[u] = c;
else
dstptr[src.cols - 1 - u] = c;
}
}
}
template <int VIEW = 0>
static void symmetricCensus9x7(const cv::Mat& src, cv::Mat& dst)
{
CV_Assert(dst.elemSize() == 4);
memset(dst.data, 0, dst.rows * dst.cols * sizeof(uint32_t));
const int RADIUS_U = 9 / 2;
const int RADIUS_V = 7 / 2;
int v;
OMP_PARALLEL_FOR
for (v = RADIUS_V; v < src.rows - RADIUS_V; v++)
{
uint32_t* dstptr = dst.ptr<uint32_t>(v);
for (int u = RADIUS_U; u < src.cols - RADIUS_U; u++)
{
uint32_t c = 0;
for (int dv = -RADIUS_V; dv <= -1; dv++)
{
for (int du = -RADIUS_U; du <= RADIUS_U; du++)
{
const int v1 = v + dv;
const int v2 = v - dv;
const int u1 = u + du;
const int u2 = u - du;
c <<= 1;
c += src.ptr(v1)[u1] <= src.ptr(v2)[u2] ? 0 : 1;
}
}
{
int dv = 0;
for (int du = -RADIUS_U; du <= -1; du++)
{
const int v1 = v + dv;
const int v2 = v - dv;
const int u1 = u + du;
const int u2 = u - du;
c <<= 1;
c += src.ptr(v1)[u1] <= src.ptr(v2)[u2] ? 0 : 1;
}
}
if (VIEW == 0)
dstptr[u] = c;
else
dstptr[src.cols - 1 - u] = c;
}
}
}
#ifdef WITH_SSE
static inline void calcMatchingCost16(__m128i _census1, const uint32_t* census2, uchar* MC)
{
for (int i = 0; i < 16; i += 4)
{
__m128i _census2 = _mm_loadu_si128((__m128i*)&census2[i]);
__m128i _diff = _mm_xor_si128(_census1, _census2);
MC[i + 0] = static_cast<uchar>(popcnt32(_mm_extract_epi32(_diff, 0)));
MC[i + 1] = static_cast<uchar>(popcnt32(_mm_extract_epi32(_diff, 1)));
MC[i + 2] = static_cast<uchar>(popcnt32(_mm_extract_epi32(_diff, 2)));
MC[i + 3] = static_cast<uchar>(popcnt32(_mm_extract_epi32(_diff, 3)));
}
}
static inline void calcMatchingCost16(__m128i _census1, const uint64_t* census2, uchar* MC)
{
for (int i = 0; i < 16; i += 2)
{
__m128i _census2 = _mm_loadu_si128((__m128i*)&census2[i]);
__m128i _diff = _mm_xor_si128(_census1, _census2);
MC[i + 0] = static_cast<uchar>(popcnt64(_mm_extract_epi64(_diff, 0)));
MC[i + 1] = static_cast<uchar>(popcnt64(_mm_extract_epi64(_diff, 1)));
}
}
#endif
template <typename T>
static inline void updateCost(T census1, const T* census2, const uchar* Lp, uchar* Lc, int u, int n, int P1, int P2)
{
#ifdef WITH_SSE
__m128i _minLp = _mm_set1_epi8(-1);
for (int d = 0; d < n; d += 16)
{
__m128i _Lp = _mm_load_si128((__m128i*)&Lp[d]);
_minLp = _mm_min_epu8(_minLp, _Lp);
}
const uchar minLp = _mm_hmin_epu8(_minLp);
P1 -= minLp;
const __m128i _census1 = _mm_set1_epi_(census1);
const __m128i _P1 = _mm_set1_epi8(P1);
const __m128i _P2 = _mm_set1_epi8(P2);
const __m128i _INF = _mm_set1_epi8(255 - P1);
_minLp = _mm_set1_epi8(minLp);
alignas(16) uchar MC[16];
for (int d = 0; d < n; d += 16)
{
if (u >= n - 1)
{
calcMatchingCost16(_census1, census2 + d, MC);
}
else
{
for (int i = 0; i < 16; i++)
MC[i] = u - (d + i) >= 0 ? HammingDistance(census1, census2[d + i]) : DEFAULT_MC;
}
const __m128i _MC = _mm_load_si128((__m128i*)MC);
__m128i _Lp0 = _mm_load_si128((__m128i*)&Lp[d]);
__m128i _Lp1 = d > 0 ? _mm_loadu_si128((__m128i*)&Lp[d - 1]) : _mm_alignr_epi8(_Lp0, _INF, 15);
__m128i _Lp2 = d < n - 16 ? _mm_loadu_si128((__m128i*)&Lp[d + 1]) : _mm_alignr_epi8(_INF, _Lp0, 1);
_Lp0 = _mm_sub_epi8(_Lp0, _minLp);
_Lp1 = _mm_add_epi8(_Lp1, _P1);
_Lp2 = _mm_add_epi8(_Lp2, _P1);
_Lp0 = _mm_min_epu8(_Lp0, _P2);
_Lp1 = _mm_min_epu8(_Lp1, _Lp2);
_Lp0 = _mm_min_epu8(_Lp0, _Lp1);
const __m128i _Lc = _mm_adds_epu8(_MC, _Lp0);
_mm_store_si128((__m128i*)&Lc[d], _Lc);
}
#else
uchar minLp = std::numeric_limits<uchar>::max();
for (int d = 0; d < n; d++)
minLp = std::min(minLp, Lp[d]);
uchar _P1 = P1 - minLp;
for (int d = 0; d < n; d++)
{
const uchar MC = u - d >= 0 ? HammingDistance(census1, census2[d]) : DEFAULT_MC;
const uchar Lp0 = Lp[d] - minLp;
const uchar Lp1 = d > 0 ? Lp[d - 1] + _P1 : 0xFF;
const uchar Lp2 = d < n - 1 ? Lp[d + 1] + _P1 : 0xFF;
const uchar Lp3 = P2;
Lc[d] = static_cast<uchar>(MC + min4(Lp0, Lp1, Lp2, Lp3));
}
#endif
}
template <typename T>
static inline void updateCost(T census1, const T* census2, uchar* Lc, int u, int n)
{
for (int d = 0; d < n; d++)
{
const int MC = u - d >= 0 ? HammingDistance(census1, census2[d]) : DEFAULT_MC;
Lc[d] = MC;
}
}
template <typename T>
static void scanCost(const cv::Mat& C1, const cv::Mat& C2, cv::Mat1b& L, int P1, int P2, int ru, int rv)
{
const int h = L.size[0];
const int w = L.size[1];
const int n = L.size[2];
const bool forward = rv > 0 || (rv == 0 && ru > 0);
int u0 = 0, u1 = w, du = 1, v0 = 0, v1 = h, dv = 1;
if (!forward)
{
u0 = w - 1; u1 = -1; du = -1;
v0 = h - 1; v1 = -1; dv = -1;
}
for (int vc = v0; vc != v1; vc += dv)
{
const T* _census1 = C1.template ptr<T>(vc);
const T* _census2 = C2.template ptr<T>(vc) + w - 1;
for (int uc = u0; uc != u1; uc += du)
{
const int vp = vc - rv;
const int up = uc - ru;
const bool inside = vp >= 0 && vp < h && up >= 0 && up < w;
uchar* _Lc = L.ptr<uchar>(vc, uc);
uchar* _Lp = (uchar*)(L.data + vp * L.step.p[0] + up * L.step.p[1]); // for CV_DbgAssert avoidance
if (inside)
updateCost(_census1[uc], _census2 - uc, _Lp, _Lc, uc, n, P1, P2);
else
updateCost(_census1[uc], _census2 - uc, _Lc, uc, n);
}
}
}
static inline int winnerTakesAll(const uchar* L0, const uchar* L1, const uchar* L2, const uchar* L3,
const uchar* L4, const uchar* L5, const uchar* L6, const uchar* L7, ushort* S, int n)
{
int minS = std::numeric_limits<int>::max();
int disp = 0;
#ifdef WITH_SSE
__m128i _zero = _mm_setzero_si128();
for (int d = 0; d < n; d += 16)
{
__m128i _L0 = _mm_load_si128((__m128i*)&L0[d]);
__m128i _L1 = _mm_load_si128((__m128i*)&L1[d]);
__m128i _L2 = _mm_load_si128((__m128i*)&L2[d]);
__m128i _L3 = _mm_load_si128((__m128i*)&L3[d]);
__m128i _L4 = _mm_load_si128((__m128i*)&L4[d]);
__m128i _L5 = _mm_load_si128((__m128i*)&L5[d]);
__m128i _L6 = _mm_load_si128((__m128i*)&L6[d]);
__m128i _L7 = _mm_load_si128((__m128i*)&L7[d]);
// sign extension
__m128i _L0_0 = _mm_unpacklo_epi8(_L0, _zero);
__m128i _L0_1 = _mm_unpackhi_epi8(_L0, _zero);
__m128i _L1_0 = _mm_unpacklo_epi8(_L1, _zero);
__m128i _L1_1 = _mm_unpackhi_epi8(_L1, _zero);
__m128i _L2_0 = _mm_unpacklo_epi8(_L2, _zero);
__m128i _L2_1 = _mm_unpackhi_epi8(_L2, _zero);
__m128i _L3_0 = _mm_unpacklo_epi8(_L3, _zero);
__m128i _L3_1 = _mm_unpackhi_epi8(_L3, _zero);
__m128i _L4_0 = _mm_unpacklo_epi8(_L4, _zero);
__m128i _L4_1 = _mm_unpackhi_epi8(_L4, _zero);
__m128i _L5_0 = _mm_unpacklo_epi8(_L5, _zero);
__m128i _L5_1 = _mm_unpackhi_epi8(_L5, _zero);
__m128i _L6_0 = _mm_unpacklo_epi8(_L6, _zero);
__m128i _L6_1 = _mm_unpackhi_epi8(_L6, _zero);
__m128i _L7_0 = _mm_unpacklo_epi8(_L7, _zero);
__m128i _L7_1 = _mm_unpackhi_epi8(_L7, _zero);
// add costs
_L0_0 = _mm_adds_epu16(_L0_0, _L1_0);
_L0_1 = _mm_adds_epu16(_L0_1, _L1_1);
_L2_0 = _mm_adds_epu16(_L2_0, _L3_0);
_L2_1 = _mm_adds_epu16(_L2_1, _L3_1);
_L4_0 = _mm_adds_epu16(_L4_0, _L5_0);
_L4_1 = _mm_adds_epu16(_L4_1, _L5_1);
_L6_0 = _mm_adds_epu16(_L6_0, _L7_0);
_L6_1 = _mm_adds_epu16(_L6_1, _L7_1);
_L0_0 = _mm_adds_epu16(_L0_0, _L2_0);
_L0_1 = _mm_adds_epu16(_L0_1, _L2_1);
_L4_0 = _mm_adds_epu16(_L4_0, _L6_0);
_L4_1 = _mm_adds_epu16(_L4_1, _L6_1);
const __m128i _S_0 = _mm_adds_epu16(_L0_0, _L4_0);
const __m128i _S_1 = _mm_adds_epu16(_L0_1, _L4_1);
const __m128i _minS_0 = _mm_minpos_epu16(_S_0);
const __m128i _minS_1 = _mm_minpos_epu16(_S_1);
_mm_store_si128((__m128i*)&S[d + 0], _S_0);
_mm_store_si128((__m128i*)&S[d + 8], _S_1);
const int S_0 = _mm_extract_epi16(_minS_0, 0);
const int S_1 = _mm_extract_epi16(_minS_1, 0);
if (S_0 < minS)
{
minS = S_0;
disp = _mm_extract_epi16(_minS_0, 1) + d + 0;
}
if (S_1 < minS)
{
minS = S_1;
disp = _mm_extract_epi16(_minS_1, 1) + d + 8;
}
}
#else
for (int d = 0; d < n; d++)
{
S[d] = L0[d] + L1[d] + L2[d] + L3[d] + L4[d] + L5[d] + L6[d] + L7[d];
if (S[d] < minS)
{
minS = S[d];
disp = d;
}
}
#endif
return disp;
}
static inline int winnerTakesAll(const uchar* L0, const uchar* L1, const uchar* L2, const uchar* L3,
ushort* S, int n)
{
int minS = std::numeric_limits<int>::max();
int disp = 0;
#ifdef WITH_SSE
__m128i _zero = _mm_setzero_si128();
for (int d = 0; d < n; d += 16)
{
__m128i _L0 = _mm_load_si128((__m128i*)&L0[d]);
__m128i _L1 = _mm_load_si128((__m128i*)&L1[d]);
__m128i _L2 = _mm_load_si128((__m128i*)&L2[d]);
__m128i _L3 = _mm_load_si128((__m128i*)&L3[d]);
// sign extension
__m128i _L0_0 = _mm_unpacklo_epi8(_L0, _zero);
__m128i _L0_1 = _mm_unpackhi_epi8(_L0, _zero);
__m128i _L1_0 = _mm_unpacklo_epi8(_L1, _zero);
__m128i _L1_1 = _mm_unpackhi_epi8(_L1, _zero);
__m128i _L2_0 = _mm_unpacklo_epi8(_L2, _zero);
__m128i _L2_1 = _mm_unpackhi_epi8(_L2, _zero);
__m128i _L3_0 = _mm_unpacklo_epi8(_L3, _zero);
__m128i _L3_1 = _mm_unpackhi_epi8(_L3, _zero);
// add costs
_L0_0 = _mm_adds_epu16(_L0_0, _L1_0);
_L0_1 = _mm_adds_epu16(_L0_1, _L1_1);
_L2_0 = _mm_adds_epu16(_L2_0, _L3_0);
_L2_1 = _mm_adds_epu16(_L2_1, _L3_1);
const __m128i _S_0 = _mm_adds_epu16(_L0_0, _L2_0);
const __m128i _S_1 = _mm_adds_epu16(_L0_1, _L2_1);
const __m128i _minS_0 = _mm_minpos_epu16(_S_0);
const __m128i _minS_1 = _mm_minpos_epu16(_S_1);
_mm_store_si128((__m128i*)&S[d + 0], _S_0);
_mm_store_si128((__m128i*)&S[d + 8], _S_1);
const int S_0 = _mm_extract_epi16(_minS_0, 0);
const int S_1 = _mm_extract_epi16(_minS_1, 0);
if (S_0 < minS)
{
minS = S_0;
disp = _mm_extract_epi16(_minS_0, 1) + d + 0;
}
if (S_1 < minS)
{
minS = S_1;
disp = _mm_extract_epi16(_minS_1, 1) + d + 8;
}
}
#else
for (int d = 0; d < n; d++)
{
S[d] = L0[d] + L1[d] + L2[d] + L3[d];
if (S[d] < minS)
{
minS = S[d];
disp = d;
}
}
#endif
return disp;
}
static inline int WTA4Path(const std::vector<cv::Mat1b>& L, cv::Mat1w& S, int v, int u, int n)
{
ushort* _S = S.ptr<ushort>(v, u);
const uchar* _L0 = L[0].ptr<uchar>(v, u);
const uchar* _L1 = L[1].ptr<uchar>(v, u);
const uchar* _L2 = L[2].ptr<uchar>(v, u);
const uchar* _L3 = L[3].ptr<uchar>(v, u);
return winnerTakesAll(_L0, _L1, _L2, _L3, _S, n);
}
static inline int WTA8Path(const std::vector<cv::Mat1b>& L, cv::Mat1w& S, int v, int u, int n)
{
ushort* _S = S.ptr<ushort>(v, u);
const uchar* _L0 = L[0].ptr<uchar>(v, u);
const uchar* _L1 = L[1].ptr<uchar>(v, u);
const uchar* _L2 = L[2].ptr<uchar>(v, u);
const uchar* _L3 = L[3].ptr<uchar>(v, u);
const uchar* _L4 = L[4].ptr<uchar>(v, u);
const uchar* _L5 = L[5].ptr<uchar>(v, u);
const uchar* _L6 = L[6].ptr<uchar>(v, u);
const uchar* _L7 = L[7].ptr<uchar>(v, u);
return winnerTakesAll(_L0, _L1, _L2, _L3, _L4, _L5, _L6, _L7, _S, n);
}
using WinnerTakesAll = int(*)(const std::vector<cv::Mat1b>& L, cv::Mat1w& S, int v, int u, int n);
template <WinnerTakesAll wta>
static void calcDisparity(const std::vector<cv::Mat1b>& L, cv::Mat1w& S, cv::Mat& D1, cv::Mat& D2,
cv::Mat& C1, float uniquenessRatio)
{
const int DISP_SCALE = SemiGlobalMatching::DISP_SCALE;
const int DISP_INV = SemiGlobalMatching::DISP_INV;
constexpr float invGamma = 1.f / 240;
const int h = S.size[0];
const int w = S.size[1];
const int n = S.size[2];
int v;
OMP_PARALLEL_FOR
for (v = 0; v < h; v++)
{
short* _D1 = D1.ptr<short>(v);
short* _D2 = D2.ptr<short>(v);
float* _C1 = C1.ptr<float>(v);
for (int u = 0; u < w; u++)
{
ushort* _S = S.ptr<ushort>(v, u);
int disp = wta(L, S, v, u, n);
// uniqueness check
int d;
for (d = 0; d < n; d++)
{
if (uniquenessRatio * _S[d] < _S[disp] && std::abs(d - disp) > 1)
break;
}
if (d < n)
{
_D1[u] = DISP_INV;
_C1[u] = 0;
continue;
}
// sub-pixel interpolation
float confidence = 0.1f;
if (disp > 0 && disp < n - 1)
{
const int SL = _S[disp - 1];
const int SC = _S[disp];
const int SR = _S[disp + 1];
const int numer = SL - SR;
const int denom = SL - 2 * SC + SR;
disp = disp * DISP_SCALE + (DISP_SCALE * numer + denom) / (2 * denom);
confidence = invGamma * (std::max(SL, SR) - SC);
}
else
{
disp *= DISP_SCALE;
}
_D1[u] = static_cast<short>(disp);
_C1[u] = confidence;
}
// calculate right disparity
for (int u = 0; u < w; u++)
{
int minS = std::numeric_limits<int>::max();
int disp = 0;
for (int d = 0; d < n && u + d < w; d++)
{
const ushort _S = S(v, u + d, d);
if (_S < minS)
{
minS = _S;
disp = d;
}
}
_D2[u] = static_cast<short>(DISP_SCALE * disp);
}
}
}
static void LRConsistencyCheck(cv::Mat& D1, cv::Mat& D2, int max12Diff)
{
const int DISP_SHIFT = SemiGlobalMatching::DISP_SHIFT;
const int DISP_INV = SemiGlobalMatching::DISP_INV;
const int h = D1.rows;
const int w = D1.cols;
int v;
OMP_PARALLEL_FOR
for (v = 0; v < h; v++)
{
short* _D1 = D1.ptr<short>(v);
short* _D2 = D2.ptr<short>(v);
for (int u = 0; u < w; u++)
{
if (_D1[u] == DISP_INV)
continue;
const int d = _D1[u] >> DISP_SHIFT;
if (u - d >= 0 && std::abs(_D1[u] - _D2[u - d]) > max12Diff)
_D1[u] = DISP_INV;
}
}
}
SemiGlobalMatching::SemiGlobalMatching(const Parameters & param) : param_(param)
{
}
void SemiGlobalMatching::compute(const cv::Mat& I1, const cv::Mat& I2, cv::Mat& D1, cv::Mat& D2, cv::Mat& C1)
{
CV_Assert(I1.type() == CV_8U && I2.type() == CV_8U);
CV_Assert(I1.size() == I2.size());
CV_Assert(param_.numDisparities % 16 == 0);
CV_Assert(param_.pathType == SCAN_4PATH || param_.pathType == SCAN_8PATH);
const int h = I1.rows;
const int w = I1.cols;
const int n = param_.numDisparities;
const int dims[3] = { h, w, n };
const int MAX_DIRECTIONS = 8;
const int ru[MAX_DIRECTIONS] = { +1, -1, +0, +0, +1, -1, -1, +1 };
const int rv[MAX_DIRECTIONS] = { +0, +0, +1, -1, +1, +1, -1, -1 };
const int numDirections = param_.pathType == SCAN_4PATH ? 4 : 8;
L.resize(numDirections);
if (param_.censusType == CENSUS_9x7)
{
census[0].create(h, w, CV_64F);
census[1].create(h, w, CV_64F);
census9x7<0>(I1, census[0]);
census9x7<1>(I2, census[1]);
int dir;
OMP_PARALLEL_FOR
for (dir = 0; dir < numDirections; dir++)
{
L[dir].create(3, dims);
scanCost<uint64_t>(census[0], census[1], L[dir], param_.P1, param_.P2, ru[dir], rv[dir]);
}
}
else if (param_.censusType == SYMMETRIC_CENSUS_9x7)
{
census[0].create(h, w, CV_32S);
census[1].create(h, w, CV_32S);
symmetricCensus9x7<0>(I1, census[0]);
symmetricCensus9x7<1>(I2, census[1]);
int dir;
OMP_PARALLEL_FOR
for (dir = 0; dir < numDirections; dir++)
{
L[dir].create(3, dims);
scanCost<uint32_t>(census[0], census[1], L[dir], param_.P1, param_.P2, ru[dir], rv[dir]);
}
}
else
{
CV_Error(cv::Error::StsInternal, "No such mode");
}
S.create(3, dims);
D1.create(h, w, CV_16S);
D2.create(h, w, CV_16S);
C1.create(h, w, CV_32F);
if (param_.pathType == SCAN_4PATH)
calcDisparity<WTA4Path>(L, S, D1, D2, C1, param_.uniquenessRatio);
else
calcDisparity<WTA8Path>(L, S, D1, D2, C1, param_.uniquenessRatio);
if (param_.medianKernelSize > 0)
{
cv::medianBlur(D1, D1, param_.medianKernelSize);
cv::medianBlur(D2, D2, param_.medianKernelSize);
}
const int max12Diff = param_.max12Diff << DISP_SHIFT;
if (max12Diff >= 0)
{
LRConsistencyCheck(D1, D2, max12Diff);
}
}