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# Gaussian filter in image processing

Gaussian filtering is more effective at smoothing images. It has its basis in the human visual perception system. It has been found that neurons create a similar filter when processing visual images. The halftone image at left has been smoothed with a Gaussian filter and is displayed to the right The images can be upgraded utilizing digital image processing. For the upgrade of the images, filters are utilized. Gaussian filters are utilized to show the improvement of images in this task. In image processing, a Gaussian blur (also known as Gaussian smoothing) is the aftereffect of obscuring a picture by a Gaussian function From the image perspective, during Gaussian filtering each individual pixel is replaced with a Gaussian shaped blob with the same total weight as the original intensity value. This Gaussian is also called the convolution kernel. It renders small structures invisible, and smoothens sharp edges Keywords. Image processing, regularization, Gaussian filtering, approximating cubic splines. 1. Introduction Gaussian filters are widely used in multi-resolution image processing. Multi-resolution techniques typically require convolution of the image with several Gaussian filters with increasing spread

In Image processing, each element in the matrix represents a pixel attribute such as brightness or a color intensity, and the overall effect is called Gaussian blur. The Gaussian filter is non-causal which means the filter window is symmetric about the origin in the time-domain. This makes the Gaussian filter physically unrealizable A Gaussian filter is a linear filter. It's usually used to blur the image or to reduce noise. If you use two of them and subtract, you can use them for unsharp masking (edge detection). The Gaussian filter alone will blur edges and reduce contrast

### What is Gaussian filtering in image processing? - Quor

For each class, to calculate the unary potentials, we learn a Gausian mixture model with pixels as individual data points. Each pixel is represented by a vector consisting of its RGB values in the original image. A small set of hand-labeled pixels (relative to the image size), serves as the training data for the Gaussian mixture model Image ﬁltering is an ubiquitous image processing tool, which requires fast and efﬁcient computation. When the ker- nel size increases, direct computation of the kernel response requires more operations and the process becomes slow A Gaussian Filter is a low pass filter used for reducing noise (high frequency components) and blurring regions of an image. The filter is implemented as an Odd sized Symmetric Kernel (DIP version of a Matrix) which is passed through each pixel of the Region of Interest to get the desired effect

Filter the image with a Gaussian filter with standard deviation of 2. Iblur = imgaussfilt (I,2); Display the original and filtered image in a montage. montage ({I,Iblur}) title ('Original Image (Left) Vs Image Processing Basic: Gaussian and Median Filter, Separable 2D filter 1. Recap. Let F be an image and H be a filter (kernel or mask). Then Correlation performs the weighted sum of... 2. Filters in more detail. Filtering has an effect of smoothing the given image as we've seen in the previous. Figure 31, 32, 33 shows FFT of image, Butterworth high pass filter of FFT image, Gaussian high pass filter of FFT image. Now the resultant sharpened images of CT and MRI image are shown in figure 34,35,36,37. Now these sharpened images can be used in various image processing tasks, like edge detection and ridge detection Esam M.A. Hussein, in Computed Radiation Imaging, 2011 9.3.2 Gaussian Filter. A Gaussian filter has the advantage that its Fourier transform is also a Gaussian distribution centered around the zero frequency (with positive and negative frequencies at both sides). One can then control the effectiveness of the low-pass nature of the filter by adjusting its width A type of low-pass filter, Gaussian blur smoothes uneven pixel values in an image by cutting out the extreme outliers. When to use Gaussian blur. Photographers and designers choose Gaussian functions for several purposes. If you take a photo in low light, and the resulting image has a lot of noise, Gaussian blur can mute that noise. If you want to lay text over an image, a Gaussian blur can soften the image so the text stands out more clearly

### Gaussian filtering of images: A regularization approach

1. Image Processing in Python-Tutorial 3-Gaussian Filter - YouTube. Image Processing in Python-Tutorial 3-Gaussian Filter. Watch later. Share. Copy link. Info. Shopping. Tap to unmute. If playback.
2. e it for you; the optimal sigma will depend on image factors - primarily the resolution of the image and the size of your objects in it (in pixels). Also, note that Gaussian filters aren't actually meant to brighten anything; you might want to look into contrast maximization techniques - sounds like something.
3. Gaussian filtering • A Gaussian kernel gives less weight to pixels further from the center of the window! • This kernel is an approximation of a Gaussian function:! • What happens if you increase σ ? ! 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0
4. Using Gaussian filter/kernel to smooth/blur an image is a very important tool in Computer Vision. You will find many algorithms using it before actually processing the image. Today we will be Applying Gaussian Smoothing to an image using Python from scratch and not using library like OpenCV. High Level Steps: There are two steps to this process
5. Gaussian filters are used in image processing because they have a property that their support in the time domain, is equal to their support in the frequency domain. This comes about from the Gaussian being its own Fourier Transform. What are the implications of this
6. An example of low pass filter applied as an image processing tool includes: mean filter, median filter, Gaussian filter and others. All this can be simply illustrated using the scipy library.
7. The Gaussian blur is a type of image-blurring filter that uses a Gaussian function (which also expresses the normal distribution in statistics) for calculating the transformation to apply to each pixel in the image. The formula of a Gaussian function in one dimension is. G ( x ) = 1 2 π σ 2 e − x 2 2 σ 2 {\displaystyle G (x)= {\frac {1} {\sqrt.

Effects of Median Filter Original Image with Salt-and-pepper noise Linear filter removes some of the noise, but not completely. Smears noise Median filter salt-and-pepper noise and keeps image structures largely intact. But also creates small spots of flat intensity, that affect sharpnes Though it is somewhat hard to believe at the first glance, this interpretation tells you that the theoretical histogram of a noisy image (which is corrupt by the noise following the same gaussian distribution you used in filtering) is the identical to the histogram that you filtering the original histogram with that gaussian filter This is the output image after applying the Mean filter. Gaussian Filter - Gaussian filter is way similar to mean filter but, instead of mean kernel, it uses Gaussian kernel. We should input the height and width (which should be odd and positive) of the kernel along with the standard deviation to the inbuilt kernel function. import numpy as n Gaussian smoothing is low-pass filtering, which means that it suppresses high-frequency detail (noise, but also edges), while preserving the low-frequency parts of the image (i.e. those that don't vary so much). In other words, the filter blurs everything that is smaller than the filter Filter the image with anisotropic Gaussian smoothing kernels. imgaussfilt allows the Gaussian kernel to have different standard deviations along row and column dimensions. These are called axis-aligned anisotropic Gaussian filters. Specify a 2-element vector for sigma when using anisotropic filters

The Gaussian high pass filter is given as: where D0 is the cut off distance as before Example of Gaussian High Pass filter An over-processed image will look grainy and unnatural, and point sources will have dark donuts around them This paper presents the study of 2D Gaussian filter and its vitality in image processing domain. The smoothing of images using 2D Gaussian filter brings out the best outcomes as compared to the conventional filters used to the date. Furthermore, when it comes to real time implementation of filter used for the image processing; it becomes a. This paper presents the study of 2D Gaussian filter and its vitality in image processing domain. The smoothing of images using 2D Gaussian filter brings out the best outcomes as compared to the conventional filters used to the date. Furthermore, whe The Gaussian blur is a type of image processing that applies a filter on an image. This filter takes the surrounding pixels (the number of which is determined by the size of the filter) and returns a single number calculated with a weighted average based on the normal distribution

### Gaussian filter - Wikipedi

1. g instructions and a sample.
2. For Gaussian derivatives, the recommendations here still apply. If you don't use DIPimage, you probably use MATLAB's Image Processing Toolbox. This toolbox makes it really easy to do convolutions with a Gaussian in the wrong way. On three accounts. The function fspecial is used to create a convolution kernel for a Gaussian filter
3. Gaussian filters • Remove high-frequency components from the image (low-pass filter) • Convolution with self is another Gaussian • So can smooth with small-width kernel, repeat, and get same result as larger-width kernel would have • Convolving two times with Gaussian kernel of width σ i
4. read 4749 You must have heard of the Gaussian function or Gaussian mask in the image processing , but here the term is Gaussian Mixture Model

Digital Image Processing using OpenCV (Python & C++) Highlights: In this post, we will learn how to apply and use an Averaging and a Gaussian filter.We will also explain the main differences between these filters and how they affect the output image Gaussian Filtering is widely used in the field of image processing. It is used to reduce the noise of an image. In this article we will generate a 2D Gaussian Kernel. The 2D Gaussian Kernel follows the below given Gaussian Distribution. Where, y is the distance along vertical axis from the origin, x is the distance along horizontal axis from. in image processing and computer vision. It is used to eliminate useless details and noise from an image. In this paper, a hardware implementation of image ﬁltered using 2D Gaussian Filter will be present. The Gaussian ﬁlter architecture will be described using a different way to implement convolution module The image at the top is the original blurred using a Gaussian filter. The 3 images at the bottom are the result of applying the sharpening filter (18) using 3 different values of $$k$$. It can be noticed how the filter has somewhat reconstructed the details that were blurred away by the smoothing operation, even though the sharpening effect is. Image processing filters. Convolution filters. These consist of simple 3x3 or 5x5 matrix convolution filters. These filters are applied by replacing each pixel intensity by a weighted average of its neighbouring pixels. The weights that are applied to the neighbouring pixel intensities are contained in a matrix called the convolution matrix

### Why is Gaussian filter used in image filtering? What are

On the other point, the normalizes the Gaussian function so that it integrates to 1. To do it properly, instead of each pixel (for example x=1, y=2) having the value , it should have the value . Then if you did that and the matrices are large enough (even 10x10 should be enough) then the matrix values should sum to 1.0 The present work investigates the qualitative and quantitative effects of the convolution of a Gaussian function with an image. Besides the evaluation of the commonly called Gaussian-blur in the filtering of images, this work also investigates a methodology of segmentation using Gaussian blurring. Noise is inherent to the physical process of acquisition. Therefore, to know the effects of a. Description. This function operates with ROI (see Regions of Interest in Intel IPP ). These functions apply the Gaussian filter to the source image ROI. pSrc. . The kernel of the Gaussian filter is the matrix of size. kernelSize. x. kernelSize In image processing, filters are mainly used to suppress either the high frequencies in the image, i.e. smoothing the image, or the low frequencies, -> In terms of execution speed, Gaussian filtering is the fastest and Bilateral filtering is the slowest

### Apply a Gauss filter to an image with Python - GeeksforGeek

This two-step process is called the Laplacian of Gaussian (LoG) operation. But this can also be performed in one step. Instead of first smoothing an image with a Gaussian kernel and then taking its Laplace, we can obtain the Laplacian of the Gaussian kernel and then convolve it with the image As we know the Gaussian Filtering is very much useful applied in the field of image processing. It is used to reduce the noise of an image. In this section we will see how to generate a 2D Gaussian Kernel

In this post, I will explain how the Laplacian of Gaussian (LoG) filter works. Laplacian of Gaussian is a popular edge detection algorithm. Edge detection is an important part of image processing and computer vision applications. It is used to detect objects, locate boundaries, and extract features 2. Gaussian Image Processing. Gaussian blur which is also known as gaussian smoothing, is the result of blurring an image by a Gaussian function.. It is used to reduce image noise and reduce details.The visual effect of this blurring technique is similar to looking at an image through the translucent screen Image f iltering functions are often used to pre-process or adjust an image before performing more complex operations. These operations help reduce noise or unwanted variances of an image or threshold. There are three filters available in the OpenCV-Python library. Gaussian Blur Filter; Erosion Blur Filter; Dilation Blur Filter; Image Smoothing techniques help us in reducing the noise in an image This paper presents the study of 2D Gaussian filter and its vitality in image processing domain. The smoothing of images using 2D Gaussian filter brings out the best outcomes as compared to the conventional filters used to the date. Furthermore, when it comes to real time implementation of filter used for the image processing; it becomes a quite daunting task for the designers as it requires. Java DIP - Applying a Gaussian Filter. In this chapter, we apply a Gaussian filter to an image which is blurred an image. We are going to use the OpenCV GaussianBlur function to apply a Gaussian filter to the images. It can be found under the Imgproc package. Its syntax is given below -. This is the source image. This is the destination image

• In image processing, we rarely use very long filters • We compute convolution directly, instead of using 2D FFT • Filter design: For simplicity we often use separable filters, an In the plot 3 1D Gaussian attributes are shown for scales 3, 5and 7. The graph of the 2D Gaussian feature is acquired by rotatingthe 1D function graphs approximately the vertical (z)-axis. 6.1.1. Properties of the Gaussian Convolution¶ The Gaussian kernel function used in a convolution has some extremely niceproperties. Separabilit In frequency domain the homomorphic filtering process looks like: First we will construct a frequency-domain high-pass filter. There are different types of high-pass filters you can construct, such as Gaussian, Butterworth, and Chebychev filters. We will construct a simple Gaussian high-pass filter directly in the frequency domain

### 2-D Gaussian filtering of images - MATLAB imgaussfil

• 2D Gaussian Filter for Image Processing: A Study (IJSTE/ Volume 3 / Issue 06 / 005) As seen in Figure 2, the Row Buffers (which are implemented in a Dual RAM FIFO memory) are used to store the.
• Using a shader with filter () is much faster than without. Shaders require the P2D or P3D renderer in size (). Converts the image to black and white pixels depending if they are above or below the threshold defined by the level parameter. The parameter must be between 0.0 (black) and 1.0 (white). If no level is specified, 0.5 is used
• The basic model for filtering is: A G(u,v) = H(u,v)F(u,v) where F(u,v) is the Fourier transform of the image being filtered and H(u,v) is the filter transform function. Define Low-Pass Filter in Image Processing . Low pass filters only pass the low frequencies, drop the high ones. The most basic of filtering operations is called low-pass
• g Valued Associates: #945 - Slate - and #948 - Vanny.
• Fig. 13 Filtering Image with 0.025 Gaussian Noise with Gaussian Filter. V. CONCLUSIONS Engineering (IJARCSSE), ISSN: 2277 128X, Vol. 3, In this paper the digital image processing using two type

Gaussian highpass filter is one of the highpass filters that has a lowpass counterpart. Highpass filters pass through only high frequencies and attenuates low ones. Before we begin with filtering in the frequency domain, we should mention how to turn image into frequencies first. To transform image from spatial domain to frequency domain we. High-pass or Sharpening Filters High pass filters let the high frequency content of the image pass through the filter and block the low frequency content. High pass filters can be modeled by first order derivative as : A second order derivative can also be used for extracting high frequency dat To use the Gaussian filter just add the Gaussian blur to your image. blurred = cv2.GaussianBlur (image, (11, 11), 0) Then minus it from the original image. g_hpf = image - blurred. Original code taken from : Image Sharpening by High Pass Filter using Python and OpenCV. Share. Improve this answer

### [CV] 2. Image Processing Basic: Gaussian and Median Filter ..

Usually, it is achieved by convolving an image with a low pass filter that removes high-frequency content like edges from the image. In this tutorial, we will see methods of Averaging, Gaussian Blur, and Median Filter used for image smoothing and how to implement them using python OpenCV, built-in functions of cv2.blur(), cv2.GaussianBlur. Multi-dimensional Gaussian filter. Parameters image array-like. Input image (grayscale or color) to filter. sigma scalar or sequence of scalars, optional. Standard deviation for Gaussian kernel. The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes It involves two processes as pre-processing and post processing of SAR image. In preprocessing, directional smoothing and hard thresholding methods has to be followed to remove the speckle noise from radar image whereas image enhancement is performed in post processing for that hybrid Laplacian Gaussian filtering (HLGF) has been utilized

### Image Sharpening By Gaussian And Butterworth High Pass Filte

• Part 2: Filtering in the Frequency Domain (using spatial filters) Download the following image two_cats.jpg and store it in MATLAB's Current Directory. Load the image data. Create a spatial filter to get the horizontal edge of the image; Create a spatial filter to get the vertical edge of the image (read the MATLAB documentation of fspecial)
• Leow Wee Kheng (CS4243) Image Processing 1 / 29. Outline 1 Basics of Image Processing 2 Convolution & Cross Correlation 3 Applications Box Filter 1D Gaussian Filter 2D Gaussian Filter 4 Self Study 5 Exercises 6 Further Reading Leow Wee Kheng (CS4243) Image Processing 2 / 29. Basics of Image Processing
• Image manipulation and processing using Numpy and Scipy A Gaussian filter smoothes the noise out and the edges as well: >>> gauss_denoised = ndimage. gaussian_filter (noisy, 2) Most local linear isotropic filters blur the image (ndimage.uniform_filter) A median filter preserves better the edges

### Video: Gaussian Filter - an overview ScienceDirect Topic

Goals . Learn to: Blur images with various low pass filters; Apply custom-made filters to images (2D convolution) 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 noise, blurring images, etc. HPF filters help in finding edges in images Gaussian Blurring. Great! We can clearly see the continued blurring of the image due to the application of our kernel. But what if you needed to blur the image and retain the color? Let us first try to apply the convolutions per color channel

Image Filtering with Machine Learning. Image filtering is used to enhance the edges in images and reduce the noisiness of an image. This technology is used in almost all smartphones. Although improving an image using the image filtering techniques can help in the process of object detection, face recognition and all tasks involved in computer. Image processing for noise reduction Common types of noise: Mean versus Gaussian filtering Input Image Mean filtered Gaussian filtered. Filtering an impulse 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Impulse signal ab c de f gh Smoothes or blurs an image by applying a Gaussian filter to the specified image. Download Toggle navigation. Search Term. Search LEADTOOLS.com Search SDK Help Demos . Demo Types. Web Demos. Image Processing Function: Gaussian Filter. Function Name. Gaussian Filter. Description. Smoothes or blurs an image by applying a Gaussian filter to the. Digital signal processing and image processing applications require the noise free and efficient arithmetic operations. To overcome the noise problem, an efficient expanded operand decomposition (ExOD) based logarithm multiplication is proposed and applied for convolution of Gaussian smoothing filter to minimize the noise

Laplacian of Gaussian Filter. Feb 14, 2001. Lab 2. Laplacian filters are derivative filters used to find areas of rapid change (edges) in images. Since derivative filters are very sensitive to noise, it is common to smooth the image (e.g., using a Gaussian filter) before applying the Laplacian. This two-step process is call the Laplacian of. Keywords: Filtering, Gaussian filter disadvantages, Bilateral filter, MATLAB software, CIE-LAB color space. *Author for correspondence khyatiaman@gmail.com 1. Introduction Image processing pertains to the alteration and analysis of pictorial information. Common cas the image shown in Figure I-III.A zero-padding is used for the first row and last row of the image. To design the filter, different steps are considered. and also swap row b and c with a and b. we should switch Figure I-III: Iteration over the image. 1) Implementation The Gaussian filter was designed in VHDL first,as shown in Figure I-IV

### Using Gaussian blur in image processing Adob

1. Gaussian function has been frequently used in image and signal processing, especially on image denoising and edge detection. In this paper, we present an approximation model of the Gaussian.
2. Gaussian Filter • A Gaussian filters smoothens an image by calculating weighted averages in a filter box. • It is used to `blur' images and remove detail and noise. • Gives more weight at the central pixels and less weights to the neighbors. • The farther away the neighbors, the smaller the weight
3. Speaking of sharp edges, bilateral filtering is quite useful for removing the noise without smoothing the edges. Similar to Gaussian blurring, bilateral filtering also uses a gaussian filter to find the Gaussian weighted average in the neighborhood. However, it also takes pixel difference into account while blurring the nearby pixels
4. ology • filtering with masks • mean filter • Gaussian filter • general cross-correlation • convolution • median filter

### Image Processing in Python-Tutorial 3-Gaussian Filter

• Filtered image, returned as a numeric array of the same size and data type as the input image, I. Tips The value of degreeOfSmoothing corresponds to the variance of the Range Gaussian kernel of the bilateral filter 
• Gaussian Filter without using the MATLAB built_in function. Gaussian Filter is used to blur the image. It is used to reduce the noise and the image details. The Gaussian kernel's center part ( Here 0.4421 ) has the highest value and intensity of other pixels decrease as the distance from the center part increases
• Outline 1 Basics of Image Processing 2 Convolution & Cross Correlation 3 Applications Box Filter 1D Gaussian Filter 2D Gaussian Filter 4 Self Study 5 Exercises 6 Further Reading Leow Wee Kheng (CS4243) Image Processing 2 / 2

### Optimal sigma for Gaussian filtering of an image

1. Hanning Filter The Hanning filter is a relatively simple low-pass filter which is described by one parameter, the cut-off (critical) frequency (Figure 5) []. The Hanning filter is defined in the frequency domain as follows: where are the spatial frequencies of the image and the cut-off (critical) frequency. In signal processing, the Hann window is a window function, called the Hann function.
2. Create a image filtering algorithm and generate hybrid images from two distinct images by filtering them with gaussian filter. python3 laplacian-pyramid gaussian-filter image-filtering high-pass-filter low-pass-filter hybrid-images. Updated on Jul 17, 2019. Python
3. How to apply Gaussian Filter? After applying the Gaussian filter to an image that it blurs an image. To apply Gaussian filter to images we need to use OpenCV function and it can be found under Imgproc package. Its syntax is given below

When using this filter, images can be processed in the X and Y directions separately or together. sobel_x_filtered_image = cv2.Sobel Canny edge detector minimises noise detection by first applying the Gaussian filter to smoothens images before proceeding with processing Gaussian Filter generation using C/C++. Gaussian filtering is extensively used in Image Processing to reduce the noise of an image. In this article I will generate the 2D Gaussian Kernel that follows the Gaussian Distribution which is given. Where σ is the standard deviation of distribution, x is the distance from the origin in the horizontal. The Gaussian filter is widely used in image processing for noise reduction, blurring, and edge detection. It is a low-pass filter and attenuates the high-frequency noise in the image. The one-dimensional Gaussian function is defined as In EBImage: Image processing and analysis toolbox for R. Description Usage Arguments Details Value Author(s) See Also Examples. View source: R/gblur.R. Description. Filters an image with a low-pass Gaussian filter. Usag

938 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 12, NO. 8, AUGUST 2003 Fast Anisotropic Gauss Filtering Jan-Mark Geusebroek, Arnold W. M. Smeulders, Member, IEEE, and Joost van de Weijer Abstract— We derive the decomposition of the anisotropic Gaussian in a one-dimensional (1-D) Gauss filter in the -direc Now we can see clearly that the image is blurry. So, this is the first method to make the image blurry. Gaussian Blur: In this approach, we do not use a standard kernel with an equal filter coefficient. Instead, we use the Gaussian Kernel. In the Gaussian kernel, we should specify the width and height of the kernel GaussianFilter is a filter commonly used in image processing for smoothing, reducing noise, and computing derivatives of an image. It is a convolution-based filter that uses a Gaussian matrix as its underlying kernel. Gaussian filtering is linear, meaning it replaces each pixel by a linear combination of its neighbors (in this case with weights specified by a Gaussian matrix) Figure 4: Filtered Images. Median Filtering Median ltering is a nonlinear ltering process primarily used to remove impulsive or salt & pepper type noise. Similar to the spatial ltering, median lter operation involves sliding a window encompassing an odd number of pixels. The center pixel in the window is then replaced by th Next, let's turn to the Gaussian part of the Gaussian blur. Gaussian blur is simply a method of blurring an image through the use of a Gaussian function. You may have heard the term Gaussian before in reference to a Gaussian distribution (a.k.a. normal distribution). Below, you'll see a 2D Gaussian distribution   In lidaRtRee: Forest Analysis with Airborne Laser Scanning (LiDAR) Data. Description Usage Arguments Value See Also Examples. View source: R/tree_detection.R. Description. applies two filters to an image: A non-linear filter: closing (mclosing) with disk kernel, or median (medianblur) with square kernel A 2D Gaussian smoother (The deriche filter is applied on both dimensions) The order of the filter along each axis is given as a sequence of integers, or as a single number. An order of 0 corresponds to convolution with a Gaussian kernel. A positive order corresponds to convolution with that derivative of a Gaussian. The array in which to place the output, or the dtype of the returned array Image Processing 101 Chapter 2.3: Spatial Filters (Convolution) In the last post, we discussed gamma transformation, histogram equalization, and other image enhancement techniques. The commonality of these methods is that the transformation is directly related to the pixel gray value, independent of the neighborhood in which the pixel is located Noise Reduction - Since edge detection is susceptible to noise in the image, the first step is to remove the noise in the image with a 5x5 Gaussian filter. Intensity Gradient - Smoothened image is then filtered with a Sobel kernel in both horizontal and vertical directions to get the first derivative in the horizontal direction (Gx) and. A Gaussian blur is implemented by convolving an image by a Gaussian distribution. Other blurs are generally implemented by convolving the image by other distributions. The simplest blur is the box blur, and it uses the same distribution we described above, a box with unit area. If we want to blur a 10x10 area, then we multiply each sample in. Below is the image convolved with $$\sigma$$ = 0.01, 1.0, 5.0, and 10.0. That's basically it, but there are some little tweaks we could add. First, notice how the Gaussian naturally tapers out; we can exploit this to functionalize the kernel size based on the inputted sigma value