收藏 | Pytorch实现Canny边缘检测

客官°小女子只卖身不卖艺 2022-09-16 12:26 49阅读 0赞

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转载于：作者 | Axel Thevenot

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![2459bd0d85c450b8229173fc86a16935.png][]

**Canny滤波器**当然是最著名和最常用的边缘检测滤波器。我会逐步解释用于**轮廓检测的canny滤波器**。因为canny滤波器是一个多级滤波器。Canny过滤器很少被集成到深度学习模型中。所以我将描述不同的部分，同时使用**Pytorch**实现它。它可以几乎没有限制的进行定制，我允许自己一些偏差。

![c202be015e49352167c2a1bac50ccc1c.png][] ![61cb353ddeb5ad561809ea5162c2b606.png][] 使用输入图像和kernel进行卷积

我来介绍一下什么是卷积矩阵，或者说核。卷积矩阵描述了我们要传递给输入图像的一个滤波器。为了简单起见，kernel将通过应用一个**卷积**，从左到右，从上到下移动整个图像。这个操作的输出称为**图像滤波**。

## 高斯滤波器 ##

首先，我们通常通过应用一个模糊滤波器来消除输入图像中的噪声。这个滤波器的选择取决于你，但我们通常使用一个**高斯**滤波器。

![a4a6be8c18fd6e8efbb8ef734d7f195f.png][] 高斯核

def get_gaussian_kernel(k=3, mu=0, sigma=1, normalize=True):
        # compute 1 dimension gaussian
        gaussian_1D = np.linspace(-1, 1, k)
        # compute a grid distance from center
        x, y = np.meshgrid(gaussian_1D, gaussian_1D)
        distance = (x ** 2 + y ** 2) ** 0.5
    
        # compute the 2 dimension gaussian
        gaussian_2D = np.exp(-(distance - mu) ** 2 / (2 * sigma ** 2))
        gaussian_2D = gaussian_2D / (2 * np.pi *sigma **2)
    
        # normalize part (mathematically)
        if normalize:
            gaussian_2D = gaussian_2D / np.sum(gaussian_2D)
        return gaussian_2D

可以制作不同大小的高斯核，或多或少都是居中或扁平的。显然，kernel越大，输出的图像越容易模糊。

![93b253f2ba350eb902dcd152e6601daa.png][]

## Sobel 滤波 ##

为了检测边缘，必须对图像应用一个滤波器来提取梯度。

![19b4b912937e48f7c861e3873e90bf1c.png][] 在X上应用Sobel kernel

def get_sobel_kernel(k=3):
        # get range
        range = np.linspace(-(k // 2), k // 2, k)
        # compute a grid the numerator and the axis-distances
        x, y = np.meshgrid(range, range)
        sobel_2D_numerator = x
        sobel_2D_denominator = (x ** 2 + y ** 2)
        sobel_2D_denominator[:, k // 2] = 1  # avoid division by zero
        sobel_2D = sobel_2D_numerator / sobel_2D_denominator
        return sobel_2D

![a06950770dc7aaba07eb0c93c62c607e.png][]

最常用的滤波器是Sobel滤波器。分解成两个滤波器，第一个核用于提取水平梯度。粗略地说，右边的像素比左边的像素越亮，过滤后的图像的结果就越高。反之亦然。这在Lena帽子的左边可以清楚地看到。

![f7915cd64429fcda2df076fb46b41cf1.png][] Y方向应用Sobel kernel

第二个核用于提取垂直的梯度。这个kernel是另一个的转置。这两个kernel具有相同的作用，但在不同的轴上。

![4f86bf4ae0f2588b82442bb7748ec5aa.png][]

## 计算梯度 ##

现在，我们在图像的两个轴上都有了梯度。为了检测轮廓，我们需要梯度的**大小**。我们可以使用绝对值范数或**欧几里得范数**。

![e6d76dbccff1c21055267ceced9d3057.png][] 梯度的大小和方向

边缘现在使用我们的梯度的大小被完美地检测，但是很厚。如果我们能只保留轮廓的细线就好了。因此，我们同时计算我们的梯度的方向，这将用于保持这些细线。在Lena的图像中，梯度是由强度表示的，因为梯度的角度非常重要。

## 非极大值抑制 ##

为了细化边缘，可以使用非最大抑制方法。在此之前，我们需要创建**45°× 45°方向的kernel**。

![7ce5ccc5c2ab26d807af9c5184a5147d.png][] 有方向的kernel ![3b6570cd75b44b0b0fba686e6a6a3a30.png][]

def get_thin_kernels(start=0, end=360, step=45):
            k_thin = 3  # actual size of the directional kernel
            # increase for a while to avoid interpolation when rotating
            k_increased = k_thin + 2
    
            # get 0° angle directional kernel
            thin_kernel_0 = np.zeros((k_increased, k_increased))
            thin_kernel_0[k_increased // 2, k_increased // 2] = 1
            thin_kernel_0[k_increased // 2, k_increased // 2 + 1:] = -1
    
            # rotate the 0° angle directional kernel to get the other ones
            thin_kernels = []
            for angle in range(start, end, step):
                (h, w) = thin_kernel_0.shape
                # get the center to not rotate around the (0, 0) coord point
                center = (w // 2, h // 2)
                # apply rotation
                rotation_matrix = cv2.getRotationMatrix2D(center, angle, 1)
                kernel_angle_increased = cv2.warpAffine(thin_kernel_0, rotation_matrix, (w, h), cv2.INTER_NEAREST)
    
                # get the k=3 kerne
                kernel_angle = kernel_angle_increased[1:-1, 1:-1]
                is_diag = (abs(kernel_angle) == 1)      # because of the interpolation
                kernel_angle = kernel_angle * is_diag   # because of the interpolation
                thin_kernels.append(kernel_angle)
            return thin_kernels

因此，该过程要求检查**8邻域**(或称为Moore的邻域)。这个概念很容易理解。对于每个像素，我们将**检查方向**。我们要看看这个像素是否比它的邻居的梯度方向更强。如果是，那么我们将其与相反方向的相邻像素进行比较。如果这个像素与它的双向邻居相比具有**最大强度**，那么它是**局部最大**。这个像素将被**保存**。在所有其他情况下，它不是一个局部最大值，像素被删除。

![2d961a6335a78b31788d0daee61e5ef0.png][]![c1ce5ac9b480adc8d7a8a0f6d10105ed.png][]

## 阈值和滞后 ##

最后，只需要应用**阈值**。有三种方法可以做到这一点:

*  **低-高**阈值：将亮度高于阈值的像素设为1，其他设为0。
 *  **低-弱**和**弱-高**阈值：我们设置高强度像素为1，低强度像素为0，介于两个阈值之间，我们设置它们为0.5，并被认为是弱像素。
 *  **低-弱**和**弱-高**与**滞后**：同上，弱像素滞后进行评估，并重新分配为高或低。

![aa7544ba9aa72c14cf687ae5cbbc1ff1.png][] 阈值

> “滞后是系统状态对其历史的依赖。”—— 维基百科

在我们的例子中，滞后可以理解为一个像素对其相邻像素的依赖。在Canny滤波器的滞后步骤中，我们说如果一个弱像素在它的8个邻居中有一个高强度的邻居，那么它将被归类为高。

我喜欢使用不同的方法，我最后使用一个滤波器对弱像素进行分类。如果它的卷积乘积**大于1**那么我把它归为High。

![42e0b91bce0969cdec8307c20e70e824.png][] 滞后kernel

## 你说过用PyTorch的 ##

是的，现在可以看看**Pytorch代码**了。所有的东西都被组合成一个**nn.Module**。我不能保证实现会得到优化。使用OpenCV的特性可以加快处理速度。但是这种实现至少具有灵活、可参数化和根据需要容易修改的优点。

class CannyFilter(nn.Module):
        def __init__(self,
                     k_gaussian=3,
                     mu=0,
                     sigma=1,
                     k_sobel=3,
                     use_cuda=False):
            super(CannyFilter, self).__init__()
            # device
            self.device = 'cuda' if use_cuda else 'cpu'
    
            # gaussian
    
            gaussian_2D = get_gaussian_kernel(k_gaussian, mu, sigma)
            self.gaussian_filter = nn.Conv2d(in_channels=1,
                                             out_channels=1,
                                             kernel_size=k_gaussian,
                                             padding=k_gaussian // 2,
                                             bias=False)
            self.gaussian_filter.weight[:] = torch.from_numpy(gaussian_2D)
    
            # sobel
    
            sobel_2D = get_sobel_kernel(k_sobel)
            self.sobel_filter_x = nn.Conv2d(in_channels=1,
                                            out_channels=1,
                                            kernel_size=k_sobel,
                                            padding=k_sobel // 2,
                                            bias=False)
            self.sobel_filter_x.weight[:] = torch.from_numpy(sobel_2D)
    
    
            self.sobel_filter_y = nn.Conv2d(in_channels=1,
                                            out_channels=1,
                                            kernel_size=k_sobel,
                                            padding=k_sobel // 2,
                                            bias=False)
            self.sobel_filter_y.weight[:] = torch.from_numpy(sobel_2D.T)
    
    
            # thin
    
            thin_kernels = get_thin_kernels()
            directional_kernels = np.stack(thin_kernels)
    
            self.directional_filter = nn.Conv2d(in_channels=1,
                                                out_channels=8,
                                                kernel_size=thin_kernels[0].shape,
                                                padding=thin_kernels[0].shape[-1] // 2,
                                                bias=False)
            self.directional_filter.weight[:, 0] = torch.from_numpy(directional_kernels)
    
            # hysteresis
    
            hysteresis = np.ones((3, 3)) + 0.25
            self.hysteresis = nn.Conv2d(in_channels=1,
                                        out_channels=1,
                                        kernel_size=3,
                                        padding=1,
                                        bias=False)
            self.hysteresis.weight[:] = torch.from_numpy(hysteresis)
    
    
        def forward(self, img, low_threshold=None, high_threshold=None, hysteresis=False):
            # set the setps tensors
            B, C, H, W = img.shape
            blurred = torch.zeros((B, C, H, W)).to(self.device)
            grad_x = torch.zeros((B, 1, H, W)).to(self.device)
            grad_y = torch.zeros((B, 1, H, W)).to(self.device)
            grad_magnitude = torch.zeros((B, 1, H, W)).to(self.device)
            grad_orientation = torch.zeros((B, 1, H, W)).to(self.device)
    
            # gaussian
    
            for c in range(C):
                blurred[:, c:c+1] = self.gaussian_filter(img[:, c:c+1])
    
                grad_x = grad_x + self.sobel_filter_x(blurred[:, c:c+1])
                grad_y = grad_y + self.sobel_filter_y(blurred[:, c:c+1])
    
            # thick edges
    
            grad_x, grad_y = grad_x / C, grad_y / C
            grad_magnitude = (grad_x ** 2 + grad_y ** 2) ** 0.5
            grad_orientation = torch.atan(grad_y / grad_x)
            grad_orientation = grad_orientation * (360 / np.pi) + 180 # convert to degree
            grad_orientation = torch.round(grad_orientation / 45) * 45  # keep a split by 45
    
            # thin edges
    
            directional = self.directional_filter(grad_magnitude)
            # get indices of positive and negative directions
            positive_idx = (grad_orientation / 45) % 8
            negative_idx = ((grad_orientation / 45) + 4) % 8
            thin_edges = grad_magnitude.clone()
            # non maximum suppression direction by direction
            for pos_i in range(4):
                neg_i = pos_i + 4
                # get the oriented grad for the angle
                is_oriented_i = (positive_idx == pos_i) * 1
                is_oriented_i = is_oriented_i + (positive_idx == neg_i) * 1
                pos_directional = directional[:, pos_i]
                neg_directional = directional[:, neg_i]
                selected_direction = torch.stack([pos_directional, neg_directional])
    
                # get the local maximum pixels for the angle
                is_max = selected_direction.min(dim=0)[0] > 0.0
                is_max = torch.unsqueeze(is_max, dim=1)
    
                # apply non maximum suppression
                to_remove = (is_max == 0) * 1 * (is_oriented_i) > 0
                thin_edges[to_remove] = 0.0
    
            # thresholds
    
            if low_threshold is not None:
                low = thin_edges > low_threshold
    
                if high_threshold is not None:
                    high = thin_edges > high_threshold
                    # get black/gray/white only
                    thin_edges = low * 0.5 + high * 0.5
    
                    if hysteresis:
                        # get weaks and check if they are high or not
                        weak = (thin_edges == 0.5) * 1
                        weak_is_high = (self.hysteresis(thin_edges) > 1) * weak
                        thin_edges = high * 1 + weak_is_high * 1
                else:
                    thin_edges = low * 1
    
    
            return blurred, grad_x, grad_y, grad_magnitude, grad_orientation, thin_edges
    —END—

原链：https://towardsdatascience.com/implement-canny-edge-detection-from-scratch-with-pytorch-a1cccfa58bed

**-------------------**

***END***

***--------------------***

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[2459bd0d85c450b8229173fc86a16935.png]: /images/20220828/6a9bd97a2171475f8103bd0fef033ee6.png
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[_ _ _]: http://mp.weixin.qq.com/s?__biz=MzU2NTc5MjIwOA==&mid=2247498631&idx=2&sn=7a91e5850ec4885a4d7028b925e6f2d2&chksm=fcb4e738cbc36e2e8ed92fcc6acbf5024ee73d4f5b2e05bcd2c31333fad86d6d4638b06fef6f&scene=21#wechat_redirect
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[PyTorch_Tensor]: http://mp.weixin.qq.com/s?__biz=MzU2NTc5MjIwOA==&mid=2247504061&idx=1&sn=207d2bd4895e0b4e303c3d9d63511c72&chksm=fcb4cc02cbc3451449159333c651688e7d71c7a744a4e4e0d914fb14adb5ad4f7e122eff7e18&scene=21#wechat_redirect
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[PyTorch_ _ 1]: http://mp.weixin.qq.com/s?__biz=MzU2NTc5MjIwOA==&mid=2247497036&idx=2&sn=552069978cf317b9581b4c9a62a003e2&chksm=fcb4e9f3cbc360e51de7a7ceb3a6adde123e488d98a3baf4204270311ef609fa5510682ff29b&scene=21#wechat_redirect
[Numpy]: https://blog.csdn.net/cxmscb/article/details/54583415
[10]: https://blog.csdn.net/lvsehaiyang1993/article/details/80342473
[CVPR 2020]: https://blog.csdn.net/u013685264/article/details/104984809
[Link 27]: https://blog.csdn.net/fengdu78/article/details/107308594
[YOLOv4]: https://blog.csdn.net/fengdu78/article/details/106450074
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