OpenCV  4.5.0-pre
Open Source Computer Vision
Image Gradients

Goal

Theory

OpenCV provides three types of gradient filters or High-pass filters, Sobel, Scharr and Laplacian. We will see each one of them.

1. Sobel and Scharr Derivatives

Sobel operators is a joint Gausssian smoothing plus differentiation operation, so it is more resistant to noise. You can specify the direction of derivatives to be taken, vertical or horizontal (by the arguments, yorder and xorder respectively). You can also specify the size of kernel by the argument ksize. If ksize = -1, a 3x3 Scharr filter is used which gives better results than 3x3 Sobel filter. Please see the docs for kernels used.

We use the functions: cv.Sobel (src, dst, ddepth, dx, dy, ksize = 3, scale = 1, delta = 0, borderType = cv.BORDER_DEFAULT)

Parameters
srcinput image.
dstoutput image of the same size and the same number of channels as src.
ddepthoutput image depth(see cv.combinations); in the case of 8-bit input images it will result in truncated derivatives.
dxorder of the derivative x.
dyorder of the derivative y.
ksizesize of the extended Sobel kernel; it must be 1, 3, 5, or 7.
scaleoptional scale factor for the computed derivative values.
deltaoptional delta value that is added to the results prior to storing them in dst.
borderTypepixel extrapolation method(see cv.BorderTypes).

cv.Scharr (src, dst, ddepth, dx, dy, scale = 1, delta = 0, borderType = cv.BORDER_DEFAULT)

Parameters
srcinput image.
dstoutput image of the same size and the same number of channels as src.
ddepthoutput image depth(see cv.combinations).
dxorder of the derivative x.
dyorder of the derivative y.
scaleoptional scale factor for the computed derivative values.
deltaoptional delta value that is added to the results prior to storing them in dst.
borderTypepixel extrapolation method(see cv.BorderTypes).

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2. Laplacian Derivatives

It calculates the Laplacian of the image given by the relation, \(\Delta src = \frac{\partial ^2{src}}{\partial x^2} + \frac{\partial ^2{src}}{\partial y^2}\) where each derivative is found using Sobel derivatives. If ksize = 1, then following kernel is used for filtering:

\[kernel = \begin{bmatrix} 0 & 1 & 0 \\ 1 & -4 & 1 \\ 0 & 1 & 0 \end{bmatrix}\]

We use the function: cv.Laplacian (src, dst, ddepth, ksize = 1, scale = 1, delta = 0, borderType = cv.BORDER_DEFAULT)

Parameters
srcinput image.
dstoutput image of the same size and the same number of channels as src.
ddepthoutput image depth.
ksizeaperture size used to compute the second-derivative filters.
scaleoptional scale factor for the computed Laplacian values.
deltaoptional delta value that is added to the results prior to storing them in dst.
borderTypepixel extrapolation method(see cv.BorderTypes).

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One Important Matter!

In our last example, output datatype is cv.CV_8U. But there is a slight problem with that. Black-to-White transition is taken as Positive slope (it has a positive value) while White-to-Black transition is taken as a Negative slope (It has negative value). So when you convert data to cv.CV_8U, all negative slopes are made zero. In simple words, you miss that edge.

If you want to detect both edges, better option is to keep the output datatype to some higher forms, like cv.CV_16S, cv.CV_64F etc, take its absolute value and then convert back to cv.CV_8U. Below code demonstrates this procedure for a horizontal Sobel filter and difference in results.

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