Linear Image Processing

Linear Image Processing by Engineers And Scientist

1. Linear Image Processing Chapter # 24 Avinash Rohra 2K12/ELE/108 Presentation of Digital Signal Processing

2. Linear Image Processing Linear image processing is based on the same two techniques as conventional Digital Signal Processing. Convolution Fourier Analysis Linear filtering can improve images in many ways : sharpening the edges of objects, reducing random noise, correcting for unequal illumination , deconvolution to correct for blur and motion, etc . These procedures are carried out by convolving the original image with an appropriate filter kernel, producing the filtered image.

3. Image Convolution A Simple Convolution is a mathematical operation on two functions (f) and (g) That producing a third Function (f * g) , that a is typically viewed a s a modified version of one of the original Functions.

4. Image convolution works in the same way as one-dimensional convolution. For instance, images can be viewed as a summation of impulses , i.e., scaled and shifted delta functions . One Dimensional Convolution

5. linear systems are characterized by how they respond to impulses; that is, by their impulse responses. T he output image from a system is equal to the input image   convolved  with the system's impulse response . The two-dimensional delta function is an image composed of all zeros, except for a single pixel at: row = 0, column = 0, which has a value of one. Delta Function One Dimensional Picture 1

6.  Assume that the row and column indexes can have both positive and negative values, such that the one is centered in a vast sea of zeros. When the delta function is passed through a linear system, the single nonzero point will be changed into some other two-dimensional pattern. Delta Function After Passing Through a Linear System 1 1 -1 -1/8 -1/8 -1/8 -1/8 1 -1/8 -1/8 -1/8 -1/8 Delta Function Shift and Subtract Edge Detection

7. Humans and other animals use vision to identify nearby objects, such as enemies, food, and mates. Same here the Picture has it’s own brightness and colors to easily view by a human  image that slowly changes from dark to light, producing a blurry and poorly defined edge.

8. Applications which we can use in Cameras : Pillbox : Pillbox has a circular top and straight Sides pillbox is the point Spread function of an out-of-focus lens

9. For example, if the lens of a camera is not properly focused, each point in the image will be projected to a circular spot on the image sensor

10. The Gaussian is the Point Spread Function of imaging systems limited by random imperfections. For instance, the image from a Camera is blurred by atmospheric turbulence, causing each point of light to become a Gaussian in the final image. Gaussian :

11. Gaussian Function we can use in different Software's to apply Effect of Gaussian Blur.

12.  3×3 operations is an image acquired by an airport x-ray baggage scanner. When this image is convolved with a 3×3 delta function (a one surrounded by 8 zeros), the image remains unchanged.  1

13. 3 3 Edge Modification  The image convolved with a 3×3 kernel consisting of a one, a negative one, and 7 zeros. This is called the  shift and subtract operation, because a shifted version of the image (corresponding to the -1) is subtracted from the original image (corresponding to the 1). 1 1 -1

14.   This processing produces the optical illusion that some objects are closer or farther away than the background, making a 3D or embossed effect. 3 3 Edge Modification   Edge detection  PSF, and the resulting image. Every edge in the original image is transformed into narrow dark and light bands that run parallel to the original edge. Thresholding this image can isolate either the dark or light band, providing a simple algorithm for detecting the edges in an image.. -1/8 -1/8 -1/8 -1/8 1 -1/8 -1/8 -1/8 -1/8

15. Edge enhancement this is sometimes called a sharpening operation ,the objects have good contrast (an appropriate level of darkness and lightness) but very blurry edges. The objects have absolutely no contrast, but very sharp edges.  3 3 Edge Modification

16. Convolution By Separable This is a technique for fast convolution, as long as the PSF is separable. A Point Spread Function is said to be separable if it can be broken into two one-dimensional signals: a vertical and a horizontal projection. x[ r,c ] = vert [r]  horz [c] where x[ r,c ] is the two-dimensional image, and vert[r] & horz[c] are the one-dimensional projections. Obviously, most images do not satisfy this requirement. For example, the pillbox is not separable. There are however an infinite number of separable images.

17. Convolution By Separable Separation of the Rectangular PSF

18. Convolution By Separable

19. Convolution By Separable An Infinite number of separable Point spread function (PSF) can be generated by defining arbitrary projections and then calculating the two dimensional function Creation of Separable PSF

20. Convolution By Separable Separation of the Gaussian

21. That’s it