Canny边缘检测是否具有旋转不变性？旋转后边缘能否被原检测器检测？

Short answer: Yes, the Canny edge detector is rotation-invariant, and it will successfully detect the rotated version of an edge it originally picked up. Let’s break down why this is true, focusing on the derivative magnitude property you mentioned:

• Gradient magnitude is rotation-invariant: The core of Canny’s edge detection relies on calculating the image gradient after Gaussian smoothing. Usually, we use operators like Sobel to compute the x-direction (Gx) and y-direction (Gy) derivatives. The gradient magnitude is calculated as sqrt(Gx² + Gy²). When you rotate an edge, the Gx' and Gy' values for the rotated edge are just the rotated components of the original Gx and Gy. Squaring these components and summing them preserves the original magnitude—so the edge strength (measured by gradient magnitude) doesn’t change with rotation.

• Non-maximum suppression adapts to rotation: While non-maximum suppression uses gradient direction to thin edges, this direction rotates along with the edge. For the rotated edge, the local gradient direction will align perfectly with the new edge orientation, so the suppression step will still correctly retain only the local maximum pixels along the edge’s direction.

• Thresholding and edge linking are unaffected: The dual thresholding step uses gradient magnitude thresholds, which we’ve established are rotation-invariant. Edge linking depends on the continuity of edge pixels, which rotation doesn’t alter—rotating an edge just shifts its position and orientation, not its connectedness.

Even with the coordinate transformation you provided (x′ = xcosθ; y′ = xsinθ), the underlying gradient magnitude calculation remains consistent across the rotated edge. The Canny detector doesn’t care about the absolute orientation of the edge—it only cares about relative changes in pixel intensity (captured by gradient magnitude) and local directionality, both of which hold up under rotation.

内容的提问来源于stack exchange，提问作者Tamuna