基于LBPH的人脸识别

1 **FaceRecognizer**


CV_EXPORTS_W Ptr<FaceRecognizer> createLBPHFaceRecognizer(int radius=1, int neighbors=8,int grid_x=8, int grid_y=8, double threshold = DBL_MAX);

Ptr<FaceRecognizer> createLBPHFaceRecognizer(int radius, int neighbors,int grid_x, int grid_y, double threshold)
{
    return new LBPH(radius, neighbors, grid_x, grid_y, threshold);
}
由代码可见LBPH使用圆形LBP算子，默认情况下，圆的半径是1，
采样点P为8，x方向和y方向上的分区个数都为8，即有8*8=64个分区，
最后一个参数为相似度阈值，待识别图像也图像库中图像相似度小于
该值时才会产生匹配结果。


2 **train**

 void LBPH::train(InputArrayOfArrays _in_src, InputArray _in_labels, bool preserveData) {
    if(_in_src.kind() != _InputArray::STD_VECTOR_MAT && _in_src.kind() != _InputArray::STD_VECTOR_VECTOR) {
        string error_message = "The images are expected as InputArray::STD_VECTOR_MAT (a std::vector<Mat>) or _InputArray::STD_VECTOR_VECTOR (a std::vector< vector<...> >).";
        CV_Error(CV_StsBadArg, error_message);
    }
    if(_in_src.total() == 0) {
        string error_message = format("Empty training data was given. You'll need more than one sample to learn a model.");
        CV_Error(CV_StsUnsupportedFormat, error_message);
    } else if(_in_labels.getMat().type() != CV_32SC1) {
        string error_message = format("Labels must be given as integer (CV_32SC1). Expected %d, but was %d.", CV_32SC1, _in_labels.type());
        CV_Error(CV_StsUnsupportedFormat, error_message);
    }
    // get the vector of matrices
    vector<Mat> src;
    _in_src.getMatVector(src);
    // get the label matrix
    Mat labels = _in_labels.getMat();
    // check if data is well- aligned
    if(labels.total() != src.size()) {
        string error_message = format("The number of samples (src) must equal the number of labels (labels). Was len(samples)=%d, len(labels)=%d.", src.size(), _labels.total());
        CV_Error(CV_StsBadArg, error_message);
    }
    // if this model should be trained without preserving old data, delete old model data
    if(!preserveData) {
        _labels.release();
        _histograms.clear();
    }
    // append labels to _labels matrix
    for(size_t labelIdx = 0; labelIdx < labels.total(); labelIdx++) {
        _labels.push_back(labels.at<int>((int)labelIdx));
    }
    // store the spatial histograms of the original data
    for(size_t sampleIdx = 0; sampleIdx < src.size(); sampleIdx++) {
        // calculate lbp image
        Mat lbp_image = elbp(src[sampleIdx], _radius, _neighbors);
        // get spatial histogram from this lbp image
        Mat p = spatial_histogram(
                lbp_image, /* lbp_image */
                static_cast<int>(std::pow(2.0, static_cast<double>(_neighbors))), /* number of possible patterns */
                _grid_x, /* grid size x */
                _grid_y, /* grid size y */
                true);
        // add to templates
        _histograms.push_back(p);
    }
}

由代码可见LBPH使用圆形LBP算子，默认情况下，
圆的半径是1，采样点P为8，x方向和y方向上的分区个数都为8，
即有8*8=64个分区，最后一个参数为相似度阈值，
待识别图像也图像库中图像相似度小于该值时才会产生匹配结果。

3 **elbp和spatial_histogram**

template <typename _Tp> static
inline void elbp_(InputArray _src, OutputArray _dst, int radius, int neighbors) {
    //get matrices
    Mat src = _src.getMat();
    // allocate memory for result
    _dst.create(src.rows-2*radius, src.cols-2*radius, CV_32SC1);
    Mat dst = _dst.getMat();
    // zero
    dst.setTo(0);
    for(int n=0; n<neighbors; n++) {
        // sample points
        float x = static_cast<float>(radius * cos(2.0*CV_PI*n/static_cast<float>(neighbors)));
        float y = static_cast<float>(-radius * sin(2.0*CV_PI*n/static_cast<float>(neighbors)));
        // relative indices
        int fx = static_cast<int>(floor(x));
        int fy = static_cast<int>(floor(y));
        int cx = static_cast<int>(ceil(x));
        int cy = static_cast<int>(ceil(y));
        // fractional part
        float ty = y - fy;
        float tx = x - fx;
        // set interpolation weights
        float w1 = (1 - tx) * (1 - ty);
        float w2 =      tx  * (1 - ty);
        float w3 = (1 - tx) *      ty;
        float w4 =      tx  *      ty;
        // iterate through your data
        for(int i=radius; i < src.rows-radius;i++) {
            for(int j=radius;j < src.cols-radius;j++) {
                // calculate interpolated value
                float t = static_cast<float>(w1*src.at<_Tp>(i+fy,j+fx) + w2*src.at<_Tp>(i+fy,j+cx) + w3*src.at<_Tp>(i+cy,j+fx) + w4*src.at<_Tp>(i+cy,j+cx));
                // floating point precision, so check some machine-dependent epsilon
                dst.at<int>(i-radius,j-radius) += ((t > src.at<_Tp>(i,j)) || (std::abs(t-src.at<_Tp>(i,j)) < std::numeric_limits<float>::epsilon())) << n;
            }
        }
    }
}

static void elbp(InputArray src, OutputArray dst, int radius, int neighbors)
{
    int type = src.type();
    switch (type) {
    case CV_8SC1:   elbp_<char>(src,dst, radius, neighbors); break;
    case CV_8UC1:   elbp_<unsigned char>(src, dst, radius, neighbors); break;
    case CV_16SC1:  elbp_<short>(src,dst, radius, neighbors); break;
    case CV_16UC1:  elbp_<unsigned short>(src,dst, radius, neighbors); break;
    case CV_32SC1:  elbp_<int>(src,dst, radius, neighbors); break;
    case CV_32FC1:  elbp_<float>(src,dst, radius, neighbors); break;
    case CV_64FC1:  elbp_<double>(src,dst, radius, neighbors); break;
    default:
        string error_msg = format("Using Original Local Binary Patterns for feature extraction only works on single-channel images (given %d). Please pass the image data as a grayscale image!", type);
        CV_Error(CV_StsNotImplemented, error_msg);
        break;
    }
}

static Mat
histc_(const Mat& src, int minVal=0, int maxVal=255, bool normed=false)
{
    Mat result;
    // Establish the number of bins.
    int histSize = maxVal-minVal+1;
    // Set the ranges.
    float range[] = { static_cast<float>(minVal), static_cast<float>(maxVal+1) };
    const float* histRange = { range };
    // calc histogram
    calcHist(&src, 1, 0, Mat(), result, 1, &histSize, &histRange, true, false);
    // normalize
    if(normed) {
        result /= (int)src.total();
    }
    return result.reshape(1,1);
}

static Mat histc(InputArray _src, int minVal, int maxVal, bool normed)
{
    Mat src = _src.getMat();
    switch (src.type()) {
        case CV_8SC1:
            return histc_(Mat_<float>(src), minVal, maxVal, normed);
            break;
        case CV_8UC1:
            return histc_(src, minVal, maxVal, normed);
            break;
        case CV_16SC1:
            return histc_(Mat_<float>(src), minVal, maxVal, normed);
            break;
        case CV_16UC1:
            return histc_(src, minVal, maxVal, normed);
            break;
        case CV_32SC1:
            return histc_(Mat_<float>(src), minVal, maxVal, normed);
            break;
        case CV_32FC1:
            return histc_(src, minVal, maxVal, normed);
            break;
        default:
            CV_Error(CV_StsUnmatchedFormats, "This type is not implemented yet."); break;
    }
    return Mat();
}


static Mat spatial_histogram(InputArray _src, int numPatterns,
                             int grid_x, int grid_y, bool /*normed*/)
{
    Mat src = _src.getMat();
    // calculate LBP patch size
    int width = src.cols/grid_x;
    int height = src.rows/grid_y;
    // allocate memory for the spatial histogram
    Mat result = Mat::zeros(grid_x * grid_y, numPatterns, CV_32FC1);
    // return matrix with zeros if no data was given
    if(src.empty())
        return result.reshape(1,1);
    // initial result_row
    int resultRowIdx = 0;
    // iterate through grid
    for(int i = 0; i < grid_y; i++) {
        for(int j = 0; j < grid_x; j++) {
            Mat src_cell = Mat(src, Range(i*height,(i+1)*height), Range(j*width,(j+1)*width));
            Mat cell_hist = histc(src_cell, 0, (numPatterns-1), true);
            // copy to the result matrix
            Mat result_row = result.row(resultRowIdx);
            cell_hist.reshape(1,1).convertTo(result_row, CV_32FC1);
            // increase row count in result matrix
            resultRowIdx++;
        }
    }
    // return result as reshaped feature vector
    return result.reshape(1,1);
}

//------------------------------------------------------------------------------
// wrapper to cv::elbp (extended local binary patterns)
//------------------------------------------------------------------------------

static Mat elbp(InputArray src, int radius, int neighbors) {
    Mat dst;
    elbp(src, dst, radius, neighbors);
    return dst;
}

 需要注意的是在求图像中每个位置的8个采样点的值时，
 是使用的采样点四个角上相应位置的加权平均值才作为
 采样点的值（见上面函数elbp_中12~35行处代码），
 这样做能降低噪音点对LBP值的影响。
 而spatial_histogram函数把最后的分区直方图结果reshape成一行，这样做能方便识别时的相似度计算。


4 **predict**   
void LBPH::predict(InputArray _src, int &minClass, double &minDist) const {
    if(_histograms.empty()) {
        // throw error if no data (or simply return -1?)
        string error_message = "This LBPH model is not computed yet. Did you call the train method?";
        CV_Error(CV_StsBadArg, error_message);
    }
    Mat src = _src.getMat();
    // get the spatial histogram from input image
    Mat lbp_image = elbp(src, _radius, _neighbors);
    Mat query = spatial_histogram(
            lbp_image, /* lbp_image */
            static_cast<int>(std::pow(2.0, static_cast<double>(_neighbors))), /* number of possible patterns */
            _grid_x, /* grid size x */
            _grid_y, /* grid size y */
            true /* normed histograms */);
    // find 1-nearest neighbor
    minDist = DBL_MAX;
    minClass = -1;
    for(size_t sampleIdx = 0; sampleIdx < _histograms.size(); sampleIdx++) {
        double dist = compareHist(_histograms[sampleIdx], query, CV_COMP_CHISQR);
        if((dist < minDist) && (dist < _threshold)) {
            minDist = dist;
            minClass = _labels.at<int>((int) sampleIdx);
        }
    }
}

函数中7~15行是计算带预测图片_src的分区直方图query，
19~25行的for循环分别比较query和人脸库直方图数组_histograms中
每一个直方图的相似度（比较方法正是CV_COMP_CHISQR），
并把相似度最小的作为最终结果，
该部分也可以看成创建LBPH类时threshold的作用，
即相似度都不小于threshold阈值则识别失败。