# Digital Image Processing. Lecture # 6 Corner Detection & Color Processing

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1 Digital Image Processing Lecture # 6 Corner Detection & Color Processing 1

2 Corners

3 Corners (interest points) Unlike edges, corners (patches of pixels surrounding the corner) do not necessarily correspond to the geometric entities of the observed scene They capture corner structures in the pattern of intensities Prove stable in a sequence of images, hence, help in tracking objects across sequences Good for correspondence algorithms in Stereopsis, structure from motion and reconstruction Corners are specific locations in the image like, mountain peaks, building corners, and interestingly shaped patches of snow. Permit matching even in the presence of occlusion (clutter) and large scale and orientation changes. 3

4 Local measures of uniqueness Suppose we only consider a small window of pixels What defines whether a feature is a good or bad candidate? Slide adapted from Darya Frolova, Denis Simakov, Weizmann Institute.

5 Feature detection Local measure of feature uniqueness How does the window change when you shift it? Shifting the window in any direction causes a big change flat region: no change in all directions edge : no change along the edge direction corner : significant change in all directions Slide adapted from Darya Frolova, Denis Simakov, Weizmann Institute.

6 Feature detection: the math Consider shifting the window W by (u,v) how do the pixels in W change? compare each pixel before and after by summing up the squared differences (SSD) this defines an SSD error of E(u,v): W

7 Small motion assumption Taylor Series expansion of I: If the motion (u,v) is small, then first order approx is good Plugging this into the formula on the previous slide

8 Feature detection: the math Consider shifting the window W by (u,v) how do the pixels in W change? compare each pixel before and after by summing up the squared differences this defines an error of E(u,v): W

9 Feature detection: the math This can be rewritten: For the example above You can move the center of the green window to anywhere on the blue unit circle Which directions will result in the largest and smallest E values? We can find these directions by looking at the eigenvectors of H

10 Quick eigenvalue/eigenvector review The eigenvectors of a matrix A are the vectors x that satisfy: The scalar is the eigenvalue corresponding to x The eigenvalues are found by solving: In our case, A = H is a 2x2 matrix, so we have The solution: Once you know, you find x by solving

11 Feature detection: the math This can be rewritten: x - x + Eigenvalues and eigenvectors of H Define shifts with the smallest and largest change (E value) x + = direction of largest increase in E. + = amount of increase in direction x + x - = direction of smallest increase in E. - = amount of increase in direction x +

12 Feature detection: the math How are +, x +, -, and x + relevant for feature detection? What s our feature scoring function?

13 Feature detection: the math How are +, x +, -, and x + relevant for feature detection? What s our feature scoring function? Want E(u,v) to be large for small shifts in all directions the minimum of E(u,v) should be large, over all unit vectors [u v] this minimum is given by the smaller eigenvalue ( - ) of H

14 Feature detection summary Here s what you do Compute the gradient at each point in the image Create the H matrix from the entries in the gradient Compute the eigenvalues. Find points with large response ( - > threshold) Choose those points where - is a local maximum as features

15 Feature detection summary Here s what you do Compute the gradient at each point in the image Create the H matrix from the entries in the gradient Compute the eigenvalues. Find points with large response ( - > threshold) Choose those points where - is a local maximum as features

16 Szeliski 2005 use harmonic mean The trace is the sum of the diagonals, i.e., trace(h) = h 11 + h 22 Very similar to - but less expensive (no square root). (That method relies on 1/square root of - ) Lots of other detectors

17 Harris Detector Harris and Stephens (Harris & Stephens, 1988) : Down weights edge like features Measure of corner response: trace 2 R det M k M det M trace M (k empirical constant, k = ) 17

18 Harris Detector: Mathematics R depends only on eigenvalues of M R is large for a corner R is negative with large magnitude for an edge R is small for a flat region Edge R < 0 Corner R > 0 Flat R small Edge R < 0 18

19 The Harris operator Harris operator

20 Harris detector example

21 f value (red high, blue low)

22 Threshold (f > value)

23 Find local maxima of f

24 Harris features (in red)

25 COLOR IMAGE PROCESSING

26 COLOR IMAGE PROCESSING Color Importance Color is an excellent descriptor Suitable for object Identification and Extraction Discrimination Humans can distinguish thousands of color shades and intensities but few shades of gray levels Color Image Processing Full-Color Processing Color is acquired with a full-color sensor Pseudo-Color Processing Assigning colors to monochrome images 26

27 COLOR FUNDAMENTALS Colors that humans perceive in an object are determined by the nature of the light reflected from the object Visible light is composed of a relatively narrow band of frequencies in the electromagnetic spectrum A body that reflects light that is balanced in all visible wavelengths appears white to the observer A body that favours reflectance in a limited range of the visible spectrum exhibits some shades of color Green objects reflect light with wavelengths primarily in the 500 to 570 nm range while absorbing most of the energy at other wavelengths 27

28 HUMAN PERSCEPTION OF COLOR Retina contains receptors Cones Day vision, can perceive color tone Red, green, and blue cones Rods Night vision, perceive brightness only Color sensation Luminance (brightness) Chrominance Hue (color tone) Saturation (color purity) 28

29 Monochromatic images Image processing - static images - Monochromatic static image - continuous image function f(x,y) arguments - two co-ordinates (x,y) Digital image functions - represented by matrices co-ordinates = integer numbers Cartesian (horizontal x axis, vertical y axis) OR (row, column) matrices Monochromatic image function range lowest value - black highest value - white Limited brightness values = gray levels

30 Colour Chromatic images Represented by vector not scalar Red, Green, Blue (RGB) Hue, Saturation, Value (HSV) luminance, chrominance (Yuv, Luv)

31 PRIMARY AND SECONDARY COLORS OF LIGHT AND PIGMENTS The primary colors can be added to produce the secondary colors of light The primary colors of light and primary colors of pigments are different For pigments, a primary color is defined as one that absorbs a primary color of light and reflects the other two Therefore, the primary colors of pigments are magenta, cyan, and yellow 31

32 Color Model COLOR MODELS Specify colors in a standard way A coordinate system that each color is represented by a single point. Most used models: RGB model (Monitor/TV) CMY model (3-color Printers) HSI model (Color Image Processing and Description) 32

33 Pixel Depth: The number of bits used to represent each pixel in RGB space. Full-color image: 24- bit RGB color image. (R, G, B) = (8 bits, 8 bits, 8 bits) Number of colors: RGB COLOR MODEL ,777,

34

35 COLOR IMAGE - RGB Color Image G-Channel 35

36 CMY Model Color Printer, Color Copier RGB data to CMY B G R Y M C 1 1 1

37 HSI COLOR MODEL Human description of color is Hue, Saturation and Brightness: Hue represents dominant color as perceived by an observer. It is an attribute associated with the dominant wavelength. Saturation refers to the relative purity or the amount of white light mixed with a hue. The pure spectrum colors are fully saturated. Pure colors are fully saturated. Pink is less saturated. Intensity reflects the brightness. 37

38 HSI Color Model The HSI model uses three measures to describe colors: Hue: A color attribute that describes a pure color (pure yellow, orange or red) Saturation: Gives a measure of how much a pure color is diluted with white light Intensity: Intensity is the same achromatic notion that we have seen in grey level images

39 HSI Color Model Intensity can be extracted from RGB images Remember the diagonal on the RGB color cube that we saw previously ran from black to white Now consider if we stand this cube on the black vertex and position the white vertex directly above it

40 HSI Color Model The intensity component of any color can be determined by passing a plane perpendicular to the intensity axis and containing the color point The intersection of the plane with the intensity axis gives us the intensity component of the color

41 HSI Color Model Hue Intensity Saturation

42 HSI COLOR MODEL- SINGLE HUE 42

43 HSI Color Model Because the only important things are the angle and the length of the saturation vector this plane is also often represented as a circle or a triangle

44 HSI Color Model

45 HSI Color Model

46 Converting from RGB to HSI 1 cos 1 2 R G R B R G 2 R B G B H if B G 360 if B G 1 2 S 1 3 min R R,G,B I 1 G B R G B 3

47

48 48 COLOR IMAGE - HSI

49 Manipulating Images In The HSI Model In order to manipulate an image under the HSI model we: First convert it from RGB to HSI Perform our manipulations under HSI Finally convert the image back from HSI to RGB RGB Image HSI Image RGB Image Manipulations

50 Pseudocolor Image Processing Pseudocolor (also called false color) image processing consists of assigning colors to grey values based on a specific criterion The principle use of pseudocolor image processing is for human visualization

51 Pseudo Color Image Processing Intensity Slicing Intensity slicing and color coding is one of the simplest kinds of pseudocolor image processing First we consider an image as a 3D function mapping spatial coordinates to intensities (that we can consider heights) Now consider placing planes at certain levels parallel to the coordinate plane If a value is one side of such a plane it is rendered in one color, and a different color if on the other side

52 Pseudo Color Image Processing Intensity Slicing

53 Pseudo Color Image Processing Intensity Slicing In general intensity slicing can be summarized as: Let [0, L-1] represent the grey scale Let l 0 represent black [f(x, y) = 0] and let l L-1 represent white [f(x, y) = L-1] Suppose P planes perpendicular to the intensity axis are defined at levels l 1, l 2,, l p Assuming that 0 < P < L-1 then the P planes partition the grey scale into P + 1 intervals V 1, V 2,,V P+1

54 Pseudo Color Image Processing Intensity Slicing Grey level color assignments can then be made according to the relation: f (x,y) c k if f (x,y) V k where c k is the color associated with the k th intensity level V k defined by the partitioning planes at l = k 1 and l = k

55 Pseudo Color Image Processing Intensity Slicing

56 Pseudo Color Image Processing Intensity Slicing

57 COLOR IMAGE - SMOOTHING Smoothing can be viewed as a spatial filtering operation in which the coefficients of the filtering mask are all 1 s This concept can be easily extended to the processing of full-color images Simply smooth each of the RGB color planes and then combine the processed planes to form a smoothed full-color result 57

58 K-Means Clustering 1. Chose the number (K) of clusters and randomly select the centroids of each cluster. 2. For each data point: Calculate the distance from the data point to each cluster. Assign the data point to the closest cluster. 3. Recompute the centroid of each cluster. 4. Repeat steps 2 and 3 until there is no further change in the assignment of data points (or in the centroids). 10/30/2014 Image Segmentation 58

59 K-Means Clustering 10/30/2014 Image Segmentation 59

60 K-Means Clustering 10/30/2014 Image Segmentation 60

61 K-Means Clustering 10/30/2014 Image Segmentation 61

62 K-Means Clustering 10/30/2014 Image Segmentation 62

63 K-Means Clustering 10/30/2014 Image Segmentation 63

64 K-Means Clustering 10/30/2014 Image Segmentation 64

65 K-Means Clustering 10/30/2014 Image Segmentation 65

66 K-Means Clustering 10/30/2014 Image Segmentation 66

67 K-Means Clustering 10/30/2014 Image Segmentation 67

68 Clustering Example 10/30/2014 Image Segmentation 68

69 Clustering Example 10/30/2014 Image Segmentation 69

70 Clustering Example 10/30/2014 Image Segmentation 70

71 Clustering Example 10/30/2014 Image Segmentation 71

72 Clustering Example D. Comaniciu and P. Meer, Robust Analysis of Feature Spaces: Color Image Segmentation, /30/2014 Image Segmentation 72

73 K-Means Clustering Example Original K=5 K=11 10/30/2014 Image Segmentation 73

74 Mean Shift Segmentation Results: 74

75 Readings from Book (3 rd Edn.) Color Processing Chapter-6 Corner Detection: Chapter-4, Computer Vision: Algorithms and Applications by Richard Szeliski

76 Material in these slides has been taken from, the following resources Acknowledgements Digital Image Processing, Rafael C. Gonzalez & Richard E. Woods, Addison-Wesley, 2002 Computer Vision: Algorithms and Applications Richard Szeliski 76

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