OpenCV  3.4.12-dev
Open Source Computer Vision
Smoothing Images

Goals

2D Convolution ( Image Filtering )

As in one-dimensional signals, images also can be filtered with various low-pass filters(LPF), high-pass filters(HPF) etc. LPF helps in removing noises, blurring the images etc. HPF filters helps in finding edges in the images.

OpenCV provides a function cv.filter2D() to convolve a kernel with an image. As an example, we will try an averaging filter on an image. A 5x5 averaging filter kernel will look like below:

\[K = \frac{1}{25} \begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 \end{bmatrix}\]

We use the functions: cv.filter2D (src, dst, ddepth, kernel, anchor = new cv.Point(-1, -1), delta = 0, borderType = cv.BORDER_DEFAULT)

Parameters
srcinput image.
dstoutput image of the same size and the same number of channels as src.
ddepthdesired depth of the destination image.
kernelconvolution kernel (or rather a correlation kernel), a single-channel floating point matrix; if you want to apply different kernels to different channels, split the image into separate color planes using split and process them individually.
anchoranchor of the kernel that indicates the relative position of a filtered point within the kernel; the anchor should lie within the kernel; default value new cv.Point(-1, -1) means that the anchor is at the kernel center.
deltaoptional value added to the filtered pixels before storing them in dst.
borderTypepixel extrapolation method(see cv.BorderTypes).

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Image Blurring (Image Smoothing)

Image blurring is achieved by convolving the image with a low-pass filter kernel. It is useful for removing noises. It actually removes high frequency content (eg: noise, edges) from the image. So edges are blurred a little bit in this operation. (Well, there are blurring techniques which doesn't blur the edges too). OpenCV provides mainly four types of blurring techniques.

1. Averaging

This is done by convolving image with a normalized box filter. It simply takes the average of all the pixels under kernel area and replace the central element. This is done by the function cv.blur() or cv.boxFilter(). Check the docs for more details about the kernel. We should specify the width and height of kernel. A 3x3 normalized box filter would look like below:

\[K = \frac{1}{9} \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}\]

We use the functions: cv.blur (src, dst, ksize, anchor = new cv.Point(-1, -1), borderType = cv.BORDER_DEFAULT)

Parameters
srcinput image; it can have any number of channels, which are processed independently, but the depth should be CV_8U, CV_16U, CV_16S, CV_32F or CV_64F.
dstoutput image of the same size and type as src.
ksizeblurring kernel size.
anchoranchor point; anchor = new cv.Point(-1, -1) means that the anchor is at the kernel center.
borderTypeborder mode used to extrapolate pixels outside of the image(see cv.BorderTypes).

cv.boxFilter (src, dst, ddepth, ksize, anchor = new cv.Point(-1, -1), normalize = true, borderType = cv.BORDER_DEFAULT)

Parameters
srcinput image.
dstoutput image of the same size and type as src.
ddepththe output image depth (-1 to use src.depth()).
ksizeblurring kernel size.
anchoranchor point; anchor = new cv.Point(-1, -1) means that the anchor is at the kernel center.
normalizeflag, specifying whether the kernel is normalized by its area or not.
borderTypeborder mode used to extrapolate pixels outside of the image(see cv.BorderTypes).
Note
If you don't want to use normalized box filter, use cv.boxFilter(). Pass an argument normalize = false to the function.

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2. Gaussian Blurring

In this, instead of box filter, gaussian kernel is used.

We use the function: cv.GaussianBlur (src, dst, ksize, sigmaX, sigmaY = 0, borderType = cv.BORDER_DEFAULT)

Parameters
srcinput image; the image can have any number of channels, which are processed independently, but the depth should be CV_8U, CV_16U, CV_16S, CV_32F or CV_64F.
dstoutput image of the same size and type as src.
ksizeblurring kernel size.
sigmaXGaussian kernel standard deviation in X direction.
sigmaYGaussian kernel standard deviation in Y direction; if sigmaY is zero, it is set to be equal to sigmaX, if both sigmas are zeros, they are computed from ksize.width and ksize.height, to fully control the result regardless of possible future modifications of all this semantics, it is recommended to specify all of ksize, sigmaX, and sigmaY.
borderTypepixel extrapolation method(see cv.BorderTypes).

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3. Median Blurring

Here, the function cv.medianBlur() takes median of all the pixels under kernel area and central element is replaced with this median value. This is highly effective against salt-and-pepper noise in the images. Interesting thing is that, in the above filters, central element is a newly calculated value which may be a pixel value in the image or a new value. But in median blurring, central element is always replaced by some pixel value in the image. It reduces the noise effectively. Its kernel size should be a positive odd integer.

We use the function: cv.medianBlur (src, dst, ksize)

Parameters
srcinput 1, 3, or 4 channel image; when ksize is 3 or 5, the image depth should be cv.CV_8U, cv.CV_16U, or cv.CV_32F, for larger aperture sizes, it can only be cv.CV_8U.
dstdestination array of the same size and type as src.
ksizeaperture linear size; it must be odd and greater than 1, for example: 3, 5, 7 ...
Note
The median filter uses cv.BORDER_REPLICATE internally to cope with border pixels.

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4. Bilateral Filtering

cv.bilateralFilter() is highly effective in noise removal while keeping edges sharp. But the operation is slower compared to other filters. We already saw that gaussian filter takes the a neighbourhood around the pixel and find its gaussian weighted average. This gaussian filter is a function of space alone, that is, nearby pixels are considered while filtering. It doesn't consider whether pixels have almost same intensity. It doesn't consider whether pixel is an edge pixel or not. So it blurs the edges also, which we don't want to do.

Bilateral filter also takes a gaussian filter in space, but one more gaussian filter which is a function of pixel difference. Gaussian function of space make sure only nearby pixels are considered for blurring while gaussian function of intensity difference make sure only those pixels with similar intensity to central pixel is considered for blurring. So it preserves the edges since pixels at edges will have large intensity variation.

We use the function: cv.bilateralFilter (src, dst, d, sigmaColor, sigmaSpace, borderType = cv.BORDER_DEFAULT)

Parameters
srcsource 8-bit or floating-point, 1-channel or 3-channel image.
dstoutput image of the same size and type as src.
ddiameter of each pixel neighborhood that is used during filtering. If it is non-positive, it is computed from sigmaSpace.
sigmaColorfilter sigma in the color space. A larger value of the parameter means that farther colors within the pixel neighborhood will be mixed together, resulting in larger areas of semi-equal color.
sigmaSpacefilter sigma in the coordinate space. A larger value of the parameter means that farther pixels will influence each other as long as their colors are close enough. When d>0, it specifies the neighborhood size regardless of sigmaSpace. Otherwise, d is proportional to sigmaSpace.
borderTypeborder mode used to extrapolate pixels outside of the image(see cv.BorderTypes).
Note
For simplicity, you can set the 2 sigma values to be the same. If they are small (< 10), the filter will not have much effect, whereas if they are large (> 150), they will have a very strong effect, making the image look "cartoonish". Large filters (d > 5) are very slow, so it is recommended to use d=5 for real-time applications, and perhaps d=9 for offline applications that need heavy noise filtering.

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