---

-   References :
    -   Done Reading
    -   Reading
        -   <https://nptel.ac.in/courses/106/106/106106224/> [IIT Madras Week 2 part 1]
        -   [Cornell CV lecture on Edge](https://www.cs.cornell.edu/courses/cs5670/2020sp/lectures/lec02%5Fedge.pdf)
        -   <https://szeliski.org/Book/> [Book Chapter 3]
        -   <https://www.wikiwand.com/en/Sobel%5Foperator>
        -   [Joseph Redmon Lectures](https://docs.google.com/presentation/d/1%5FZOtT17Ih2P-MRbWtZ8CTRQaJBz9V6-5%5FVA00QebiQQ/edit#slide=id.g36d6019af2%5F0%5F126)
        -   <https://evergreenllc2020.medium.com/fundamentals-of-image-gradients-and-edge-detection-b093662ade1b>
    -   To read:

-   Questions :

---

-   Criteria for a good edge detector
    -   Good detection
        -   find all real edges, ignoring noise or other artifacts
    -   Good Localization
        -   detect edges as close as possible to true edges
    -   Single Response
        -   return one point only for each true edge point

<!--listend-->

```python
from skimage.filters import roberts, sobel, scharr, prewitt, farid
roberts_img = roberts(img)
sobel_img = sobel(img)
scharr_img = scharr(img)
prewitt_img = prewitt(img)
farid_img = farid(img)
```


## Robert, Scharr, Prewitt, Farid {#robert-scharr-prewitt-farid}

<a id="orgffa4c49"></a>

{{< figure src="/ox-hugo/2021-05-30_15-35-13_screenshot.png" caption="Figure 1: from nptel [IIT Madras] CV lecture slide Week 2 part 1" width="450" height="250" target="/blogs" >}}

-   _The x-coordinate in figure ref:edge-filter-kernel is defined as increasing in the "right"-direction, and the y-coordinate is defined as increasing in the "down"-direction. At each point in the image, the resulting gradient approximations can be combined to give the gradient magnitude, using:_ [wikipedia]

    \\( {M} = \sqrt{ ({M}\_{x})^{2} + ({M}\_{y})^{2}} \\)

-   Using this information, we can also calculate the gradient's direction(orientation):

    \\( \Theta = \arctan{\frac{M\_{y}}{M\_{x}}} \\)

where, for example, \\(\Theta\\) is 0 for a vertical edge which is lighter on the right side.


## Sobel {#sobel}

{{< figure src="/ox-hugo/2021-05-30_15-43-53_screenshot.png" width="450" height="250" target="/blogs" >}}

-   Computes the image gradient in the x direction

{{< figure src="/ox-hugo/2021-05-30_15-44-40_screenshot.png" caption="Figure 2: from nptel [IIT Madras] CV lecture slide Week 2 part 1" width="450" height="250" target="/blogs" >}}

-   Computes the image gradient in the y direction


## Canny edge {#canny-edge}


### Algorithm {#algorithm}

-   Smooth image (only want “real” edges, not noise)
-   Calculate gradient direction and magnitude
-   Non-maximum suppression perpendicular to edge
    -   check if pixel is local maximum along gradient problem
-   Threshold into strong, weak, no edge
    -   Define two thresholds: low and high
    -   hysteresis:
        -   Use the high threshold to start edge curves and the low threshold to continue them
    -   if gradient at pixel > 'High' = 'edge pixel'
    -   if gradient at pixel < 'Low' = 'non edge pixel'
    -   if gradient at pixel >= 'Low' and <= 'High' = 'edge pixel' iff,
        -   it is connected to an 'edge pixel' directly or via pixels between 'Low' and 'High'
-   Connect together components
-   Tunable: Sigma, thresholds
-   Canny edge pipeline

{{< figure src="/ox-hugo/2021-05-30_19-18-30_screenshot.png" caption="Figure 3: from nptel [IIT Madras] CV lecture slide Week 2 part 1" width="900" height="210" target="/blogs" >}}

-   Effect of \\(\sigma\\) in Cannyu Edge Detector
    -   The choice of σ (Gaussian kernel spread/size) depends on desired behavior
        -   large σ detects large-scale edges
        -   small σ detects fine edges

{{< figure src="/ox-hugo/2021-05-30_20-29-59_screenshot.png" caption="Figure 4: from nptel [IIT Madras] CV lecture slide Week 2 part 1" width="600" height="250" target="/blogs" >}}


### Python implementation {#python-implementation}

```python
canny_edge = cv2.Canny(img, 50, 80)
# auto canny
sigma = 0.3
median = np.median(img)
lower = int(max(0, (1.0 - sigma) * median))
upper = int(min(255, (1.0 + sigma) * median))
auto_canny = cv2.Canny(img, lower, upper)
```