Computer Graphics Fundamentals

Transcription

1 Computer Graphics Fundamentals Jacek Kęsik, PhD

2 Simple converts Rotations Translations Flips Resizing

3 Geometry Rotation n * 90 degrees other

4 Geometry Rotation n * 90 degrees other

5 Geometry Translations Pixels cannot move We only repleace the colours of pixels. Copy and paste area of pixels to other location

6 Geometry Flips Vertical Horizontal Simple reverse of rows or columns of image

7 Non contextual Non contextual processing has two main properties: Each pixel is processed independently from its neighbours. Only the values of colour/intensity are changed. Pixels do not move. Usually all the pixels of the image are subject to the same processing

8 Non contextual In most cases it involves a calculation of new intensity of pixel, basing on the equation: L' m, n L( m, n) L(m,n) is the new intensity of pixel (m,n) in the picture For the colour images function is calculated for each of the colour values of single pixel

9 Non contextual Intensity values are in range from 0 to 255. When recalculated it can easily go out of the range. This cannot be allowed. Values off the range are trimmed to fit: Values below 0 are set to 0, values over 255 are set to 255. Usually before calculation, values of pixels are normalized to the range <0,1> and restored to original range afteralls

10 Non contextual typical processing Brightness Function L is reduced to: L' m, n L( m, n) ( and are set to 1) To all the values of pixels intensity the same amount is added.

11 Non contextual typical processing Brightness When is positive the image is lightned Negative value of makes image darker The bigger value of the more values of pixels have to be trimmed

12 Non contextual typical processing Brightness

13 Non contextual LUT table Executing of the above method would require calculation of the equation for every pixel in the image (Current standard of cameras in smartphones is 8Mpix meaning 24M times for RGB image) It s nothing serious for current processors, but that equation was the simplest one and we need to trim excesive values This is NOT the optimal solution

14 Non contextual LUT table Every pixel value is an integer from 0 to 255. So there are only 256 possible solutions of the equation! Let s calculate them all, trim and put into table called Look Up Table LUT has 2 rows: Original value Calculated value

15 Non contextual LUT table now it s only a matter of simple assignment LUT table Old pixel values New pixel values

16 Non contextual typical processing Contrast Changing contrast means increasing or decreasing differences between next values of intensities in the image it is done by multiplication of the pixel values (with a small hack) The equation L has a shape: L' m, n L( m, n) MAX MAX 0 for L( m, n) MAX MAX MAX MAX for 0 L( m, n) MAX MAX MAX for L( m, n) MAX 2 2 MAX

17 Non contextual typical processing Contrast When is smaller than 1 we get decrease of contrast. Extremely low puts all the values in exact middle of the range (gray screen) When is greater than 1 we get increase of contrast. Extremely high causes all values to be either 0 or MAX

18 Non contextual typical processing Contrast

19 Non contextual typical processing Gamma correction It is used to correct uneven brightness of the image caused by imperfect device (camera, scanner, screen) The equation can operate only on values of range <0,1> - we have to add normalization L' m, n MAX * L( m, n) MAX

20 Non contextual typical processing Gamma correction When is below 1 we increase space between darker values at the cost of squeezing brighter values When is over 1 we do the oposite L' m, n MAX * L( m, n) MAX

21 Non contextual typical processing Gamma correction

22 Non contextual typical processing Histogram Histogram is a tool aiding in using of many non contextual image processings It shows a graph of percentage of the pixels having the same intensity Bars are put in row from 0 to MAX

23 Non contextual typical processing Histogram Histogram of a well exposed image should be more or less uniform. When the weight is placed on one of the borders we can expect underexposed or overexposed image Source:

24 Non contextual typical processing Histogram usage example An image not always uses the whole intensity range. We can stretch the histogram to cover the whole range

25 Non contextual typical processing Histogram usage example An image not always uses the whole intensity range. We can stretch the histogram to cover the whole range

26 Non contextual typical processing Curves Another tool allowing to fine-tune non contextual processing. It allowes to use a combination of the above corrections without the need to set numerical values of equation parameters. It is used there where the standard simple processing gives dissapointing results

27 Non contextual typical processing Curves The tool window is a rectangle with a diagonal line. The gradient on the bottom represents original intensity values. The one to the left represents calculated values

28 Non contextual typical processing Curves The diagonal line is a representation of the equation. In its current shape it is a 1:1 conversion (nothing changes) The histogram in the background is placed to aid in choosing the right shape of the line

29 Non contextual typical processing Curves Brightness

30 Non contextual typical processing Curves Brightness

31 Non contextual typical processing Curves Contrast (wrong way)

32 Non contextual typical processing Curves Contrast (right way)

33 Non contextual typical processing Curves Contrast (right way)

34 Non contextual typical processing Curves Gamma correction

35 Non contextual typical processing Curves Gamma correction

36 Non contextual Real life case What could we adjust in this image?

37 Non contextual Real life case What shows histogram?

38 Non contextual Real life case Can we just gamma correct?

39 Non contextual Real life case How about using Curves?

40 Contextual It transforms the pixels intensities basing on the information about each pixel neighborhood.

41 Contextual The neighborhood is usually a set of 8 surrounding pixels + the one calculated -1,-1 0,-1 1,-1-1,0 0,0 1,0-1,1 0,1 1,1

42 Contextual The calculate contextual transformation we generally use convolution K j i j w i a ), ( ), ( K j i j i j n i m n m w A a A ), (, ), (, 1 ' Where w(i,j) is a weight of pixel in position i,j relative to the calculated one

43 Contextual filter examples Blur

44 Contextual filter examples Gaussian Blur

45 Contextual filter examples Laplacean Designed to strenghten edges All the weights sum up to 0

46 Contextual filter examples Laplacean

47 Contextual filter examples Edges (Sobel) Designed to find specific edges Horizontal Vertical

48 Contextual filter examples Edges (Sobel)

49 Contextual filter examples Edges (Sobel) Designed to find specific edges Diagonal

50 Contextual nonlinear filters These kind of filters not only mind the neighborhood in calculating the pixel value but also choose the transformation accordingly to neighborhood

51 Contextual nonlinear filters Combined filters Nonlinear combination of several linear filters (Eg. Several blurs and choosing the one closest to the original value)

52 Contextual nonlinear filters Statistical filters Minimum choosing the minimal value from neighborhood Maximum choosing the maximal value from neighborhood

53 Contextual nonlinear filters Statistical filters Median chooses the value from neighborhood closest to the average of them all Doesn t introduce new values into image It is used for smoothing without blurring (remooving artefacts)

54 Contextual nonlinear filters Adaptative filters Choosing the way of working depending on the neighborhood Eg an adaptative blur (two passes) 1. Finding edges (sobel) 2. Implementing gaussian blur to all pixels except found edges

55 So much for theory How about practice?