在进行高斯卷积(2d)时，边界处的急剧过渡

Sharp transition at borders when doing Gaussian Convolution (2d)

本文关键字：边界 高斯 卷积 2d      更新时间：2023-10-16

我正在尝试使用高斯二维卷积模糊矩阵。但是我在边界元素处得到了尖锐的过渡。

下面是我正在运行的一段代码:

// create 1D Kernel
void createGaussianKerenel_1D() {
    unsigned kernelSize = 2 * kernelRad_ + 1;
    gaussian1Dkernel_ = vector<double>(kernelSize);
    double sigma = (double)kernelRad_;
    double sum = 0.0;
    for(unsigned i = 0; i < kernelSize; ++i) {
        gaussian1Dkernel_[i] = gaussian(i, sigma);
        sum += gaussian1Dkernel_[i];
    }
    // normalize
    for(unsigned i = 0; i < kernelSize; ++i) {
        gaussian1Dkernel_[i] /= sum;
        cout << gaussian1Dkernel_[i] << endl;
    }
}
// gaussian function
double gaussian(unsigned int i, double sigma) const {
    double x = ((double)i - (double)kernelRad_) / sigma;
    return exp(-x * x / 2);
}
// do Separable 2D Convolution (in place)
// my initialMatrix_ is of yn_ x xn_ size
void getBlurredThermalMap() {
    assert(!gaussian1Dkernel_.empty());
    vector<vector<double> > tmpMatrix(yn_);
    unsigned kernelSize = 2 * kernelRad_ + 1;
    // in x direction
    for(unsigned i = 0; i < yn_; ++i) {
        for(unsigned j = 0; j < xn_; ++j) {
            double approxVal = 0.0;
            for(unsigned row = 0; row < kernelSize; ++row) {
                unsigned neighbor_j = j + row - kernelRad_;
                // ignore values that are out of bound
                if(neighbor_j >= 0 && neighbor_j < xn_) {
                    approxVal += initialMatrix_[i][neighbor_j] * gaussian1Dkernel_[row];
                }
            }
            tmpMatrix[i].push_back(approxVal);
        }
    }
    // in y direction
    for(unsigned j = 0; j < xn_; ++j) {
        for(unsigned i = 0; i < yn_; ++i) {
            double approxVal = 0.0;
            for(unsigned col = 0; col < kernelSize; ++col) {
                unsigned neighbor_i = i + col - kernelRad_;
                if(neighbor_i >= 0 && neighbor_i < yn_) {
                    approxVal += tmpMatrix[neighbor_i][j] * gaussian1Dkernel_[col];
                }
            }
            initialMatrix_[i][j] = approxVal;
        }
    }
}

。对于边界元素，我使用了相同的核。我已经测试了这个代码在100x100矩阵和内核2半径。例如，我在1,97和2,97处的元素之间有相当大的差异，尽管在初始矩阵中，这两个位置没有明显的过渡。

也许我需要改变核计算近似值的边界元素?

这可能是因为您没有正确处理边界条件。在你的测试中:

if(neighbor_i >= 0 && neighbor_i < yn_)

第一部分总是为真，因为neighbor_i是unsigned，因此总是正数。您可能希望将其更改为带符号的值，稍微修改其声明。你的编译器可以用适当的警告标志为你检查这些错误(试试-Wall -Wextra)。

编辑:实际上，测试可能不是您的问题的原因，因为您正在使用相对较小的图像，使neighbor_i的值大于yn_，当试图在其中存储负值时。

同样，请使用库来做卷积。特别是有相当好的和有效的近似(Canny-Deriche，傅立叶域积，…)高斯模糊

我是这样解决这个问题的:

在createGaussianKerenel_1D()函数中不要规范化内核。相反，可以在getBlurredThermalMap()函数中执行，如下所示:

void getBlurredThermalMap() {
    assert(!gaussian1Dkernel_.empty());
    vector<vector<double> > tmpMatrix(yn_);
    unsigned kernelSize = 2 * kernelRad_ + 1;
    // in x direction
    for(unsigned i = 0; i < yn_; ++i) {
        for(unsigned j = 0; j < xn_; ++j) {
            double approxVal = 0.0;
            double sumNorm = 0.0;
            for(unsigned row = 0; row < kernelSize; ++row) {
                unsigned neighbor_j = j + row - kernelRad_;
                // ignore values that are out of bound
                if(neighbor_j >= 0 && neighbor_j < xn_) {
                    approxVal += initialMatrix_[i][neighbor_j] * gaussian1Dkernel_[row];
                    sumNorm += gaussian1Dkernel_[row];
                }
            }
            approxVal /= sumNorm;
            tmpMatrix[i].push_back(approxVal);
        }
    }
    // in y direction
    for(unsigned j = 0; j < xn_; ++j) {
        for(unsigned i = 0; i < yn_; ++i) {
            double approxVal = 0.0;
            double sumNorm = 0.0;
            for(unsigned col = 0; col < kernelSize; ++col) {
                unsigned neighbor_i = i + col - kernelRad_;
                if(neighbor_i >= 0 && neighbor_i < yn_) {
                    approxVal += tmpMatrix[neighbor_i][j] * gaussian1Dkernel_[col];
                    sumNorm += gaussian1Dkernel_[row];
                }
            }
            approxVal /= sumNorm;
            initialMatrix_[i][j] = approxVal;
        }
    }
}
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