[OpenCV][纹理特征]如何计算不同方向下的高斯导数直方图

学习SelectiveSearch算法时候,其纹理特征需要计算类SIFT特征,实现方式是计算每张图片8个方向上10 bin大小的高斯导数直方图

$S_{texture}(r_{i}, r_{j})$ measures texture similarity. We represent texture using fast SIFT-like measurements as SIFT itself works well for material recognition [20]. We take Gaussian derivatives in eight orientations using $σ = 1$ for each colour channel. For each orientation for each colour channel we extract a histogram using a bin size of 10. This leads to a texture histogram $T_{i} = {t_{i}^{1}, …, t_{i}^{n}}$ for each region $r_{i}$ with dimensionality $n = 240$ when three colour channels are used. Texture histograms are normalised using the $L_{1}$ norm. Similarity is measured using histogram intersection:

OpenCV实现了SelectiveSearch算法,其通过图像旋转、Scharr滤波以及手动计算直方图的方式完成了纹理特征的计算。之前没有思考过如何完成不同方向下导数直方图的计算,学习里面代码实现不同方向下的导数直方图计算

源码地址:opencv_contrib/modules/ximgproc/src/selectivesearchsegmentation.cpp

完整流程

  1. 计算高斯导数
  2. 计算直方图
  3. 直方图连接

计算高斯导数

需要分别计算8个方向上的高斯导数,分别是

  1. x轴正/负方向
  2. y轴正/负方向
  3. 图像逆时针45度旋转后x轴正/负方向
  4. 图像逆时针45度旋转后y轴正/负方向

使用函数Scharr对图像进行高斯求导,然后通过阈值函数threshold获取正/负方向的求导结果

完成上述操作后将结果进行标准化([0,255]),以便后续直方图的计算。实现代码如下:

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/**
* 计算8个方向的高斯导数
* @param src CV_8UC1
* @param gauss_vector
*/
void calc_8_direction_guass(const Mat &src, vector<Mat> &gauss_vector) {
// cout << src.channels() << endl;

Mat gauss, gauss_pos, gauss_neg;
Mat rotated, rotated_gauss;
Mat rotated_gauss_tmp;

// x轴,向左/向右
Scharr(src, gauss, CV_32F, 1, 0);
threshold(gauss, gauss_pos, 0, 0, THRESH_TOZERO);
threshold(gauss, gauss_neg, 0, 0, THRESH_TOZERO_INV);
gauss_vector.emplace_back(gauss_pos);
gauss_vector.emplace_back(gauss_neg);

// y轴,向上/向下
gauss.release();
Scharr(src, gauss, CV_32F, 0, 1);

gauss_pos.release();
gauss_neg.release();
threshold(gauss, gauss_pos, 0, 0, THRESH_TOZERO);
threshold(gauss, gauss_neg, 0, 0, THRESH_TOZERO_INV);
gauss_vector.emplace_back(gauss_pos);
gauss_vector.emplace_back(gauss_neg);

// 逆时针旋转45度
Point2f center(src.cols / 2.0f, src.rows / 2.0f);
Mat rot = cv::getRotationMatrix2D(center, 45.0, 1.0);
Rect bbox = cv::RotatedRect(center, src.size(), 45.0).boundingRect();
rot.at<double>(0, 2) += bbox.width / 2.0 - center.x;
rot.at<double>(1, 2) += bbox.height / 2.0 - center.y;
warpAffine(src, rotated, rot, bbox.size());
// cout << rotated.size() << endl;

// 计算x轴方向导数
Scharr(rotated, rotated_gauss, CV_32F, 1, 0);

// 顺时针旋转45度,获取原先图像大小
center = Point((int) (rotated.cols / 2.0), (int) (rotated.rows / 2.0));
rot = cv::getRotationMatrix2D(center, -45.0, 1.0);
warpAffine(rotated_gauss, rotated_gauss_tmp, rot, bbox.size());
gauss = rotated_gauss_tmp(Rect((bbox.width - src.cols) / 2,
(bbox.height - src.rows) / 2, src.cols, src.rows));
gauss_pos.release();
gauss_neg.release();
threshold(gauss, gauss_pos, 0, 0, THRESH_TOZERO);
threshold(gauss, gauss_neg, 0, 0, THRESH_TOZERO_INV);
gauss_vector.emplace_back(gauss_pos);
gauss_vector.emplace_back(gauss_neg);

// 重复上一步骤
rotated_gauss.release();
Scharr(rotated, rotated_gauss, CV_32F, 0, 1);

// 顺时针旋转45度,获取原先图像大小
center = Point((int) (rotated.cols / 2.0), (int) (rotated.rows / 2.0));
rot = cv::getRotationMatrix2D(center, -45.0, 1.0);
warpAffine(rotated_gauss, rotated_gauss_tmp, rot, bbox.size());
gauss = rotated_gauss_tmp(Rect((bbox.width - src.cols) / 2,
(bbox.height - src.rows) / 2, src.cols, src.rows));
gauss_pos.release();
gauss_neg.release();
threshold(gauss, gauss_pos, 0, 0, THRESH_TOZERO);
threshold(gauss, gauss_neg, 0, 0, THRESH_TOZERO_INV);
gauss_vector.emplace_back(gauss_pos);
gauss_vector.emplace_back(gauss_neg);

// Normalisze gaussiaans in 0-255 range (for faster computation of histograms)
// 缩放图像到0-255,方便直方图计算
for (int i = 0; i < 8; i++) {
double hmin, hmax;
minMaxLoc(gauss_vector[i], &hmin, &hmax);

Mat tmp;
gauss_vector[i].convertTo(tmp, CV_8U,
255 / (hmax - hmin),
-255 * hmin / (hmax - hmin));
gauss_vector[i] = tmp;
}
}
  • 进行阈值函数操作后直接放入向量中,所以求导图像有正有负
  • 标准化公式如下:

计算直方图

参考:直方图

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/**
* 计算颜色直方图,图像取值固定为[0, 255]
* @param src CV_8UC1或CV_8UC3大小图像
* @param histograms 直方图向量
* @param bins 直方图大小
*/
void calc_color_hist(const Mat &src, vector<Mat> &histograms, int bins) {
int channels = src.channels();
vector<Mat> img_planes;
if (channels == 3) {
split(src, img_planes);
} else {
// gray
img_planes.emplace_back(src);
}

float range[] = {0, 256}; //the upper boundary is exclusive
const float *histRange = {range};
bool uniform = true, accumulate = false;

for (int i = 0; i < channels; i++) {
Mat hist, tranpose_hist;
calcHist(&img_planes[i], 1, nullptr, Mat(), hist, 1, &bins, &histRange, uniform, accumulate);
//转置图像,得到一行数据
transpose(hist, tranpose_hist);
histograms.emplace_back(tranpose_hist);
}
}

调用OpenCV函数calcHist得到的是N列大小的矩阵,为方便后续计算,将其转置成单行矩阵

直方图连接

彩色图像有3个通道,每个通道有8个方向求导,共得到3x8=24个直方图

对每个求导图像计算10 bin大小的直方图,所以得到的纹理特征维数是24x10=240

在连接各个直方图之前,可以先对其进行标准化([0,1]),以便后续操作

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int main() {
Mat src = imread("../lena.jpg");
Mat gray;
cvtColor(src, gray, COLOR_BGR2GRAY);

vector<Mat> img_planes;
split(src, img_planes);

// 得到3x8=24个高斯求导图像,取值范围在[0,255]
vector<Mat> gauss_vectors;
for (const Mat &img: img_planes) {
vector<Mat> gauss_vector;
calc_8_direction_guass(img, gauss_vector);
gauss_vectors.insert(gauss_vectors.end(), gauss_vector.begin(), gauss_vector.end());
}

// 计算10 bin大小直方图
vector<Mat> hists;
for (const Mat &img: gauss_vectors) {
vector<Mat> hist;
calc_color_hist(img, hist, 10);
hists.insert(hists.end(), hist.begin(), hist.end());
}

// 归一化直方图
for (const Mat &img: hists) {
Mat dst;
img.convertTo(dst, CV_32F, 1.0 / sum(img)[0]);
cout << dst << endl;
}

// 按行连接所有矩阵
cv::Mat out;
cv::vconcat(hists, out);
cout << out << endl;

return 0;
}
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