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| 1 | +.. _Canny: |
| 2 | + |
| 3 | +Canny Edge Detection |
| 4 | +*********************** |
| 5 | + |
| 6 | +Goal |
| 7 | +====== |
| 8 | + |
| 9 | +In this chapter, we will learn about |
| 10 | + |
| 11 | + * Concept of Canny edge detection |
| 12 | + * OpenCV functions for that : **cv2.Canny()** |
| 13 | + |
| 14 | +Theory |
| 15 | +========= |
| 16 | + |
| 17 | +Canny Edge Detection is a popular edge detection algorithm. It was developed by John F. Canny in 1986. It is a multi-stage algorithm and we will go through each stages. |
| 18 | + |
| 19 | +1. **Noise Reduction** |
| 20 | + |
| 21 | +Since edge detection is susceptible to noise in the image, first step is to remove the noise in the image with a 5x5 Gaussian filter. We have already seen this in previous chapters. |
| 22 | + |
| 23 | +2. **Finding Intensity Gradient of the Image** |
| 24 | + |
| 25 | +Smoothened image is then filtered with a Sobel kernel in both horizontal and vertical direction to get first derivative in horizontal direction (:math:`G_x`) and vertical direction (:math:`G_y`). From these two images, we can find edge gradient and direction for each pixel as follows: |
| 26 | + |
| 27 | +.. math:: |
| 28 | +
|
| 29 | + Edge\_Gradient \; (G) = \sqrt{G_x^2 + G_y^2} |
| 30 | +
|
| 31 | + Angle \; (\theta) = \tan^{-1} \bigg(\frac{G_y}{G_x}\bigg) |
| 32 | +
|
| 33 | +Gradient direction is always perpendicular to edges. It is rounded to one of four angles representing vertical, horizontal and two diagonal directions. |
| 34 | + |
| 35 | +3. **Non-maximum Suppression** |
| 36 | + |
| 37 | +After getting gradient magnitude and direction, a full scan of image is done to remove any unwanted pixels which may not constitute the edge. For this, at every pixel, pixel is checked if it is a local maximum in its neighborhood in the direction of gradient. Check the image below: |
| 38 | + |
| 39 | + .. image:: images/nms.svg |
| 40 | + :alt: Non-Maximum Suppression |
| 41 | + :align: center |
| 42 | + |
| 43 | +Point A is on the edge ( in vertical direction). Gradient direction is normal to the edge. Point B and C are in gradient directions. So point A is checked with point B and C to see if it forms a local maximum. If so, it is considered for next stage, otherwise, it is suppressed ( put to zero). |
| 44 | + |
| 45 | +In short, the result you get is a binary image with "thin edges". |
| 46 | + |
| 47 | +4. **Hysteresis Thresholding** |
| 48 | + |
| 49 | +This stage decides which are all edges are really edges and which are not. For this, we need two threshold values, `minVal` and `maxVal`. Any edges with intensity gradient more than `maxVal` are sure to be edges and those below `minVal` are sure to be non-edges, so discarded. Those who lie between these two thresholds are classified edges or non-edges based on their connectivity. If they are connected to "sure-edge" pixels, they are considered to be part of edges. Otherwise, they are also discarded. See the image below: |
| 50 | + |
| 51 | + .. image:: images/hysteresis.svg |
| 52 | + :alt: Hysteresis Thresholding |
| 53 | + :align: center |
| 54 | + |
| 55 | +The edge A is above the `maxVal`, so considered as "sure-edge". Although edge C is below `maxVal`, it is connected to edge A, so that also considered as valid edge and we get that full curve. But edge B, although it is above `minVal` and is in same region as that of edge C, it is not connected to any "sure-edge", so that is discarded. So it is very important that we have to select `minVal` and `maxVal` accordingly to get the correct result. |
| 56 | + |
| 57 | +This stage also removes small pixels noises on the assumption that edges are long lines. |
| 58 | + |
| 59 | +So what we finally get is strong edges in the image. |
| 60 | + |
| 61 | +Canny Edge Detection in OpenCV |
| 62 | +=============================== |
| 63 | + |
| 64 | +OpenCV puts all the above in single function, **cv2.Canny()**. We will see how to use it. First argument is our input image. Second and third arguments are our `minVal` and `maxVal` respectively. Third argument is `aperture_size`. It is the size of Sobel kernel used for find image gradients. By default it is 3. Last argument is `L2gradient` which specifies the equation for finding gradient magnitude. If it is ``True``, it uses the equation mentioned above which is more accurate, otherwise it uses this function: :math:`Edge\_Gradient \; (G) = |G_x| + |G_y|`. By default, it is ``False``. |
| 65 | +:: |
| 66 | + |
| 67 | + import cv2 |
| 68 | + import numpy as np |
| 69 | + from matplotlib import pyplot as plt |
| 70 | + |
| 71 | + img = cv2.imread('messi5.jpg',0) |
| 72 | + edges = cv2.Canny(img,100,200) |
| 73 | + |
| 74 | + plt.subplot(121),plt.imshow(img,cmap = 'gray') |
| 75 | + plt.title('Original Image'), plt.xticks([]), plt.yticks([]) |
| 76 | + plt.subplot(122),plt.imshow(edges,cmap = 'gray') |
| 77 | + plt.title('Edge Image'), plt.xticks([]), plt.yticks([]) |
| 78 | + |
| 79 | + plt.show() |
| 80 | + |
| 81 | +See the result below: |
| 82 | + |
| 83 | + .. image:: images/canny1.jpg |
| 84 | + :alt: Canny Edge Detection |
| 85 | + :align: center |
| 86 | + |
| 87 | +Additional Resources |
| 88 | +======================= |
| 89 | + |
| 90 | +#. Canny edge detector at `Wikipedia <http://en.wikipedia.org/wiki/Canny_edge_detector>`_ |
| 91 | +#. `Canny Edge Detection Tutorial <http://dasl.mem.drexel.edu/alumni/bGreen/www.pages.drexel.edu/_weg22/can_tut.html>`_ by Bill Green, 2002. |
| 92 | + |
| 93 | + |
| 94 | +Exercises |
| 95 | +=========== |
| 96 | + |
| 97 | +#. Write a small application to find the Canny edge detection whose threshold values can be varied using two trackbars. This way, you can understand the effect of threshold values. |
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