Lecture No Image Filtering (course: Computer Vision)

Transcription

1 Lecture No Image Filtering (course: Computer Vision) e- mail: Department of So9ware Engineering, Mehran UET Jamshoro, Sind, Pakistan

2 Enhancement using Arithme0c/ Logic Opera0ons ArithmeUc/Logic operauons perform on pixel by pixel basis between two or more images Except NOT operauon which perform only on a single image NOT operauon = negauve transformauon Logic operauon performs on gray- level images, the pixel values are processed as binary numbers Light represents a binary 1, and dark represents a binary 0

3 AND Opera0on original image AND image mask result of AND operation

4 OR Opera0on original image OR image mask result of OR operation

5 Image SubtracUon

6 SpaUal Filtering SpaUal filtering can be done by making use of filter (can also be called as mask/kernel/ template or window). The values in a filter sub- image are referred to as coefficients, rather than pixel Our focus will be on masks of odd sizes, e.g. 3x3, 5x5,

7 SpaUal Filtering Process simply move the filter mask from point to point in an image At each point (x,y), the response of the filter at that point is calculated using a predefined relauonship Where z i is gray level of pixels associated with mask coefficient w i

8 Linear Filtering Linear Filtering of an image f of size MxN filter mask of size mxn is given by the expression To generate a complete filtered image this equauon must be applied for: x = 0, 1, 2,, M- 1 and y = 0, 1, 2,, N- 1

9 Used for blurring and for noise reducuon Smoothing SpaUal Filters Blurring is used in preprocessing steps, such as: removal of small details from an image prior to object extracuon bridging of small gaps in lines or curves Noise reducuon can be accomplished by blurring with a linear filter and also by a nonlinear filter Output is simply the average of the pixels contained in the neighborhood of the filter mask These are called as Averaging filters or lowpass filters

10 Smoothing SpaUal Filters Replacing the value of every pixel in an image by the average of the gray levels in the neighborhood will reduce the sharp transiuons in gray levels Sharp transiuons random noise in the image edges of objects in the image Thus, smoothing can reduce noises (desirable) and blur edges (undesirable)

11 3x3 Smoothing Linear Filters box filter weighted average the center is the most important and other pixels are inversely weighted as a funcuon of their distance from the center of the mask Weighted average Filter The basic strategy behind this technique is, weighung the center point the highest and then reducing the value of the coefficients as a funcuon of increasing distance from the origin is simply an adempt to reduce blurring in the smoothing process

12 General form of smoothing mask Filter of size mxn (m and n odd) summation of all coefficient of the mask

13 Example a). Original image 500x500 pixel b) f). Results of smoothing with square averaging filter masks of size n = 3, 5, 9, 15 and 35, respecuvely Note:- Big mask is used to eliminate small objects from an image The size of the mask establishes the relauve size of the objects that will be blended with the background

14 Example original image result after smoothing with 15x15 averaging mask result of thresholding we can see that the result a9er smoothing and thresholding, the remains are the largest and brightest objects in the image

15 Median Filters

16 Example: Median Filters

17 Sharpening SpaUal Filters To highlight fine details in an image OR - To enhance detail that has been blurred, either in error or as a natural effect of a parucular method of image acquisiuon As we know that blurring can be done in spaual domain by pixel averaging in a neighbors Since averaging is analogous to integrauon Thus, we can guess that the sharpening must be accomplished by spa0al differen0a0on

18 DerivaUve operator The strength of the response of a derivauve operator is proporuonal to the degree of disconunuity of the image at the point at which the operator is applied Thus, image differenuauon enhances edges and other disconunuiues (noise) deemphasizes area with slowly varying gray- level values

19 First- order, Second- order DerivaUve A basic definiuon of the first- order derivauve of a one- dimensional funcuon f(x) is the difference Similarly, we define the second- order derivauve of a one- dimensional funcuon f(x) is the difference

20 First- order, Second- order DerivaUve of f(x,y) when we consider an image funcuon of two variables, f(x,y), at which Ume we will dealing with parual derivauves along the two spaual axes Gradient operator Laplacian operator (linear operator)

21 Discrete Form of Laplacian from yield,

22 Result of Laplacian Mask

23 As it is a derivauve operator, it highlights gray- level disconunuiues in an image it deemphasizes regions with slowly varying gray levels Effect of Laplacian Operator Tends to produce images that have grayish edge lines and other disconunuiues, all superimposed on a dark featureless background

24 Easily by adding the original and Laplacian image Correct the effect of featureless background Be careful with the Laplacian filter used if the center coefficient of the Laplacian mask is negative if the center coefficient of the Laplacian mask is positive

25 Example a). image of the North pole of the moon. b). Laplacian- filtered image with c). Laplacian image scaled for display purposes. d). image enhanced by addiuon with original image

26 Mask of Laplacian + (addiuon) To simply the computauon, we can create a mask which do both operauons, Laplacian Filter and AddiUon the original image

27 Example

28 To be NoUced = + = +

29 Unsharp masking To subtract a blurred version of an image produces sharpening output image Use of GRADIENT operators sharpened image = original image blurred image

30 Example of Combining SpaUal Enhancement Methods want to sharpen the original image and bring out more skeletal detail Problems: narrow dynamic range of gray level and high noise content makes the image difficult to

31 Example of Combining SpaUal Enhancement Methods solve by using: 1. Laplacian to highlight fine detail 2. Gradient to enhance prominent edges 3. Gray- level transformauon to increase the dynamic range of gray levels

32 Example of Combining SpaUal Enhancement Methods

33 Example of Combining SpaUal Enhancement Methods

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