OpenCV  4.2.0
Open Source Computer Vision
Smoothing Images

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Goal

In this tutorial you will learn how to apply diverse linear filters to smooth images using OpenCV functions such as:

Theory

Note
The explanation below belongs to the book Computer Vision: Algorithms and Applications by Richard Szeliski and to LearningOpenCV
  • Smoothing, also called blurring, is a simple and frequently used image processing operation.
  • There are many reasons for smoothing. In this tutorial we will focus on smoothing in order to reduce noise (other uses will be seen in the following tutorials).
  • To perform a smoothing operation we will apply a filter to our image. The most common type of filters are linear, in which an output pixel's value (i.e. \(g(i,j)\)) is determined as a weighted sum of input pixel values (i.e. \(f(i+k,j+l)\)) :

    \[g(i,j) = \sum_{k,l} f(i+k, j+l) h(k,l)\]

    \(h(k,l)\) is called the kernel, which is nothing more than the coefficients of the filter.

    It helps to visualize a filter as a window of coefficients sliding across the image.

  • There are many kind of filters, here we will mention the most used:

Normalized Box Filter

  • This filter is the simplest of all! Each output pixel is the mean of its kernel neighbors ( all of them contribute with equal weights)
  • The kernel is below:

    \[K = \dfrac{1}{K_{width} \cdot K_{height}} \begin{bmatrix} 1 & 1 & 1 & ... & 1 \\ 1 & 1 & 1 & ... & 1 \\ . & . & . & ... & 1 \\ . & . & . & ... & 1 \\ 1 & 1 & 1 & ... & 1 \end{bmatrix}\]

Gaussian Filter

  • Probably the most useful filter (although not the fastest). Gaussian filtering is done by convolving each point in the input array with a Gaussian kernel and then summing them all to produce the output array.
  • Just to make the picture clearer, remember how a 1D Gaussian kernel look like?

    Assuming that an image is 1D, you can notice that the pixel located in the middle would have the biggest weight. The weight of its neighbors decreases as the spatial distance between them and the center pixel increases.

    Note
    Remember that a 2D Gaussian can be represented as :

    \[G_{0}(x, y) = A e^{ \dfrac{ -(x - \mu_{x})^{2} }{ 2\sigma^{2}_{x} } + \dfrac{ -(y - \mu_{y})^{2} }{ 2\sigma^{2}_{y} } }\]

    where \(\mu\) is the mean (the peak) and \(\sigma^{2}\) represents the variance (per each of the variables \(x\) and \(y\))

Median Filter

The median filter run through each element of the signal (in this case the image) and replace each pixel with the median of its neighboring pixels (located in a square neighborhood around the evaluated pixel).

Bilateral Filter

  • So far, we have explained some filters which main goal is to smooth an input image. However, sometimes the filters do not only dissolve the noise, but also smooth away the edges. To avoid this (at certain extent at least), we can use a bilateral filter.
  • In an analogous way as the Gaussian filter, the bilateral filter also considers the neighboring pixels with weights assigned to each of them. These weights have two components, the first of which is the same weighting used by the Gaussian filter. The second component takes into account the difference in intensity between the neighboring pixels and the evaluated one.
  • For a more detailed explanation you can check this link

Code

  • What does this program do?
    • Loads an image
    • Applies 4 different kinds of filters (explained in Theory) and show the filtered images sequentially

Explanation

Let's check the OpenCV functions that involve only the smoothing procedure, since the rest is already known by now.

Normalized Block Filter:

  • OpenCV offers the function blur() to perform smoothing with this filter. We specify 4 arguments (more details, check the Reference):
    • src: Source image
    • dst: Destination image
    • Size( w, h ): Defines the size of the kernel to be used ( of width w pixels and height h pixels)
    • Point(-1, -1): Indicates where the anchor point (the pixel evaluated) is located with respect to the neighborhood. If there is a negative value, then the center of the kernel is considered the anchor point.

Gaussian Filter:

  • It is performed by the function GaussianBlur() : Here we use 4 arguments (more details, check the OpenCV reference):
    • src: Source image
    • dst: Destination image
    • Size(w, h): The size of the kernel to be used (the neighbors to be considered). \(w\) and \(h\) have to be odd and positive numbers otherwise the size will be calculated using the \(\sigma_{x}\) and \(\sigma_{y}\) arguments.
    • \(\sigma_{x}\): The standard deviation in x. Writing \(0\) implies that \(\sigma_{x}\) is calculated using kernel size.
    • \(\sigma_{y}\): The standard deviation in y. Writing \(0\) implies that \(\sigma_{y}\) is calculated using kernel size.

Median Filter:

  • This filter is provided by the medianBlur() function: We use three arguments:
    • src: Source image
    • dst: Destination image, must be the same type as src
    • i: Size of the kernel (only one because we use a square window). Must be odd.

Bilateral Filter

  • Provided by OpenCV function bilateralFilter() We use 5 arguments:
    • src: Source image
    • dst: Destination image
    • d: The diameter of each pixel neighborhood.
    • \(\sigma_{Color}\): Standard deviation in the color space.
    • \(\sigma_{Space}\): Standard deviation in the coordinate space (in pixel terms)

Results

  • The code opens an image (in this case lena.jpg) and display it under the effects of the 4 filters explained.
  • Here is a snapshot of the image smoothed using medianBlur:

cv::Mat::rows
int rows
the number of rows and columns or (-1, -1) when the matrix has more than 2 dimensions
Definition: mat.hpp:2086
cv::String
std::string String
Definition: cvstd.hpp:150
cv::Mat::clone
Mat clone() const CV_NODISCARD
Creates a full copy of the array and the underlying data.
cv::IMREAD_COLOR
@ IMREAD_COLOR
If set, always convert image to the 3 channel BGR color image.
Definition: imgcodecs.hpp:67
cv::FONT_HERSHEY_COMPLEX
@ FONT_HERSHEY_COMPLEX
normal size serif font
Definition: imgproc.hpp:817
cv::samples::findFile
cv::String findFile(const cv::String &relative_path, bool required=true, bool silentMode=false)
Try to find requested data file.
cv::Mat::zeros
static MatExpr zeros(int rows, int cols, int type)
Returns a zero array of the specified size and type.
cv::waitKey
int waitKey(int delay=0)
Waits for a pressed key.
highgui.hpp
cv::namedWindow
void namedWindow(const String &winname, int flags=WINDOW_AUTOSIZE)
Creates a window.
cv::Scalar_< double >
cv::Size
Size2i Size
Definition: types.hpp:347
cv::imread
Mat imread(const String &filename, int flags=IMREAD_COLOR)
Loads an image from a file.
cv::Mat::empty
bool empty() const
Returns true if the array has no elements.
cv::Mat::cols
int cols
Definition: mat.hpp:2086
cv::medianBlur
void medianBlur(InputArray src, OutputArray dst, int ksize)
Blurs an image using the median filter.
cv::Mat::size
MatSize size
Definition: mat.hpp:2108
imgcodecs.hpp
cv::imshow
void imshow(const String &winname, InputArray mat)
Displays an image in the specified window.
cv::Scalar
Scalar_< double > Scalar
Definition: types.hpp:669
cv::GaussianBlur
void GaussianBlur(InputArray src, OutputArray dst, Size ksize, double sigmaX, double sigmaY=0, int borderType=BORDER_DEFAULT)
Blurs an image using a Gaussian filter.
cv::blur
void blur(InputArray src, OutputArray dst, Size ksize, Point anchor=Point(-1,-1), int borderType=BORDER_DEFAULT)
Blurs an image using the normalized box filter.
cv::putText
void putText(InputOutputArray img, const String &text, Point org, int fontFace, double fontScale, Scalar color, int thickness=1, int lineType=LINE_8, bool bottomLeftOrigin=false)
Draws a text string.
cv::Point
Point2i Point
Definition: types.hpp:194
cv::Mat
n-dimensional dense array class
Definition: mat.hpp:792
cv::imshow
void imshow(const String &winname, const ogl::Texture2D &tex)
Displays OpenGL 2D texture in the specified window.
cv::Mat::type
int type() const
Returns the type of a matrix element.
cv
"black box" representation of the file storage associated with a file on disk.
Definition: affine.hpp:52
cv::bilateralFilter
void bilateralFilter(InputArray src, OutputArray dst, int d, double sigmaColor, double sigmaSpace, int borderType=BORDER_DEFAULT)
Applies the bilateral filter to an image.
imgproc.hpp
cv::WINDOW_AUTOSIZE
@ WINDOW_AUTOSIZE
the user cannot resize the window, the size is constrainted by the image displayed.
Definition: highgui.hpp:184