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Sobel Edge Detection

Computer Vision

Medium

The Sobel operator detects image edges by estimating horizontal and vertical intensity changes. Given a two-dimensional grayscale image, compute the gradient magnitude at every pixel.

Pad the image with one row or column of zeros on every side. Use the following horizontal kernel:

K_x = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}

Use the following vertical kernel:

K_y = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix}

For each image position with coordinates (i, j), center both kernels on that position and compute:

G_x(i,j) = \sum_{a=0}^{2}\sum_{b=0}^{2} K_x(a,b)P(i+a,j+b)

G_y(i,j) = \sum_{a=0}^{2}\sum_{b=0}^{2} K_y(a,b)P(i+a,j+b)

Combine the two directional responses:

G(i,j) = \sqrt{G_x(i,j)^2 + G_y(i,j)^2}

Here, P is the zero-padded image, i and j identify an output pixel, and a and b identify a kernel position.

Return G as a two-dimensional list of floats with the same height and width as the input image.

Loading visualization...

Examples

Input: image = [[0, 0, 10, 10], [0, 0, 10, 10], [0, 0, 10, 10]]

Output: [[0.0, 31.622776601683793, 42.42640687119285, 42.42640687119285], [0.0, 40.0, 40.0, 40.0], [0.0, 31.622776601683793, 42.42640687119285, 42.42640687119285]]

Explanation: The vertical intensity transition produces large horizontal Sobel responses.

Input: image = [[100]]

Output: [[0.0]]

Hint 1

Copy the image into the center of a grid with a one-pixel zero border.

Hint 2

Accumulate horizontal and vertical kernel responses before taking their Euclidean magnitude.

Requirements

Apply zero-padding before convolution
Compute both Gx and Gy using the standard Sobel kernels
Return the magnitude as sqrt(Gx^2 + Gy^2) for each pixel
Output has the same dimensions as the input

Constraints

Image has at least one pixel
Pixel values are non-negative numbers
Return a 2D list of floats with the same shape as the input
Time limit: 300 ms

Try Similar Problems

Gaussian Blur Kernel Conv2d Image Filtering Morphological Operations Image Histogram Histogram Equalization

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Sobel Edge Detection

Computer Vision

Medium

The Sobel operator detects image edges by estimating horizontal and vertical intensity changes. Given a two-dimensional grayscale image, compute the gradient magnitude at every pixel.

Pad the image with one row or column of zeros on every side. Use the following horizontal kernel:

K_x = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}

Use the following vertical kernel:

K_y = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix}

For each image position with coordinates (i, j), center both kernels on that position and compute:

G_x(i,j) = \sum_{a=0}^{2}\sum_{b=0}^{2} K_x(a,b)P(i+a,j+b)

G_y(i,j) = \sum_{a=0}^{2}\sum_{b=0}^{2} K_y(a,b)P(i+a,j+b)

Combine the two directional responses:

G(i,j) = \sqrt{G_x(i,j)^2 + G_y(i,j)^2}

Here, P is the zero-padded image, i and j identify an output pixel, and a and b identify a kernel position.

Return G as a two-dimensional list of floats with the same height and width as the input image.

Loading visualization...

Examples

Input: image = [[0, 0, 10, 10], [0, 0, 10, 10], [0, 0, 10, 10]]

Output: [[0.0, 31.622776601683793, 42.42640687119285, 42.42640687119285], [0.0, 40.0, 40.0, 40.0], [0.0, 31.622776601683793, 42.42640687119285, 42.42640687119285]]

Explanation: The vertical intensity transition produces large horizontal Sobel responses.

Input: image = [[100]]

Output: [[0.0]]

Hint 1

Copy the image into the center of a grid with a one-pixel zero border.

Hint 2

Accumulate horizontal and vertical kernel responses before taking their Euclidean magnitude.

Requirements

Apply zero-padding before convolution
Compute both Gx and Gy using the standard Sobel kernels
Return the magnitude as sqrt(Gx^2 + Gy^2) for each pixel
Output has the same dimensions as the input

Constraints

Image has at least one pixel
Pixel values are non-negative numbers
Return a 2D list of floats with the same shape as the input
Time limit: 300 ms

Try Similar Problems

Gaussian Blur Kernel Conv2d Image Filtering Morphological Operations Image Histogram Histogram Equalization

Case 1

Case 2

image =

Accepts: array

The Sobel operator detects image edges by estimating horizontal and vertical intensity changes. Given a two-dimensional grayscale image, compute the gradient magnitude at every pixel.

Pad the image with one row or column of zeros on every side. Use the following horizontal kernel:

K_x = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}

Use the following vertical kernel:

K_y = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix}

For each image position with coordinates (i, j), center both kernels on that position and compute:

G_x(i,j) = \sum_{a=0}^{2}\sum_{b=0}^{2} K_x(a,b)P(i+a,j+b)

G_y(i,j) = \sum_{a=0}^{2}\sum_{b=0}^{2} K_y(a,b)P(i+a,j+b)

Combine the two directional responses:

G(i,j) = \sqrt{G_x(i,j)^2 + G_y(i,j)^2}

Here, P is the zero-padded image, i and j identify an output pixel, and a and b identify a kernel position.

Return G as a two-dimensional list of floats with the same height and width as the input image.