Digital Image Processing Lecture IV

Digital Image Processing Lecture IV PowerPoint PPT Presentation

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. . Smoothing Spatial Filters. Smoothing linear filtersAveraging filtersBox filterWeighted average filter. Smoothing Spatial Filters. The general implementation for filtering an MXN image with a weighted averaging filter of size mxn is given by where a=(m-1)/2 and b=(n-1)/2. Smoothing Spatial FiltersImage smoothing with masks of various sizes.

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Digital Image Processing Lecture IV

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1. Digital Image Processing Lecture IV Spatial Filtering (cont’d) and Image Segmentation Spring 2010

3. Smoothing linear filters Averaging filters Box filter Weighted average filter

4. The general implementation for filtering an MXN image with a weighted averaging filter of size mxn is given by where a=(m-1)/2 and b=(n-1)/2

7. Order-statistic filters Median filter: to reduce impulse noise (salt-and-pepper noise)

8. Sharpening Spatial Filters The objective is to highlight transitions in intensity. Applications vary ranging from electronic printing and medical imaging to industrial guidance in military systems.

9. Sharpening Spatial Filters An Example

10. Sharpening filters are based on computing spatial derivatives of an image. The first-order derivative of a one-dimensional function f(x) is The second-order derivative of a one-dimensional function f(x) is

11. Development of the Laplacian method The two dimensional Laplacian operator for continuous functions [Rosenfeld et. Al 1982]: The Laplacian is a linear operator.

13. To sharpen an image, the Laplacian of the image is subtracted from the original image. Example: Figure 3.40 shown next.

15. Unsharp Masking and Highboost Filtering A process that has been used for many years in printing and publishing industry to sharpen images. Blur the original image Subtract the blurred image from the original (let the resulting difference be mask) Add mask to the original

16. Unsharp Masking and Highboost Filtering Let f’(x,y) denote the blurred image gmask(x,y) = f(x,y) - f’(x,y) g(x,y) = f(x,y) + k*gmask(x,y), where k>=0 is the weight. When k=1, we have unsharp masking When k >1, the process is called highboost filtering When k < 1, it de-emphasizes the contribution of the mask.

17. 1D Unsharp Masking

18. Example

26. Image segmentation divides an image into regions that are connected and have some similarity within the region and some difference between adjacent regions. The goal is usually to find individual objects in an image. For the most part there are fundamentally two kinds of approaches to segmentation: discontinuity and similarity. Similarity may be due to pixel intensity, color or texture. Differences are sudden changes (discontinuities) in any of these, but especially sudden changes in intensity along a boundary line, which is called an edge.

27. Image Segmentation

28. Fundamentals

29. Fundamentals

30. Image Segmentation

31. Image Segmentation Example

32. There are three kinds of discontinuities of intensity: points, lines and edges. The most common way to look for discontinuities is to scan a small mask over the image. The mask determines which kind of discontinuity to look for.

33. Background The focus is to detect sharp, local changes in intensity, which can be detected using derivatives. First-, second-order derivatives are particularly well suited for this purpose. Derivatives of a digital function are defined in terms of differences.

34. Background

35. Background

37. Detection of Isolated Points

39. Only slightly more common than point detection is to find a one pixel wide line in an image. For digital images the only three point straight lines are only horizontal, vertical, or diagonal (+ or –45?).

40. Line Detection

47. Three fundamental steps in edge detection

49. Basic Edge Detection

50. Example

58. Advanced Edge Detector: The Canny Edge Detector

61. Two properties of edge points are useful for edge linking: the strength (or magnitude) of the detected edge points their directions (determined from gradient directions) This is usually done in local neighborhoods. Adjacent edge points with similar magnitude and direction are linked. For example, an edge pixel with coordinates (x0,y0) in a predefined neighborhood of (x,y) is similar to the pixel at (x,y) if

62. Edge linking with local processing

64. Regional Processing

65. Hough transform: a way of finding edge points in an image that lie along a straight line. Example: xy-plane v.s. ab-plane (parameter space)

66. Thresholding for Segmentation

67. Assumption: the range of intensity levels covered by objects of interest is different from the background.

72. Adaptive Thresholding Divide the image into sub-images. Assume that the illumination in each sub-images is constant. Use a different threshold for each sub-image. Alternatively – use a running window (and use the threshold of the window only for the central pixel )

77. Region-Based Segmentation

78. Edges and thresholds sometimes do not give good results for segmentation. Region-based segmentation is based on the connectivity of similar pixels in a region. Each region must be uniform. Connectivity of the pixels within the region is very important. There are two main approaches to region-based segmentation: region growing and region splitting.

79. Let R represent the entire image region. Segmentation is a process that partitions R into subregions, R1,R2,…,Rn, such that where P(Rk): a logical predicate defined over the points in set Rk For example: P(Rk)=TRUE if all pixels in Rk have the same gray level.

80. Fig. 10.41 shows the histogram of Fig. 10.40 (a). It is difficult to segment the defects by thresholding methods. (Applying region growing methods are better in this case.)

82. Region splitting is the opposite of region growing. First there is a large region (possible the entire image). Then a predicate (measurement) is used to determine if the region is uniform. If not, then the method requires that the region be split into two regions. Then each of these two regions is independently tested by the predicate (measurement). This procedure continues until all resulting regions are uniform.

83. The main problem with region splitting is determining where to split a region. One method to divide a region is to use a quadtree structure. Quadtree: a tree in which nodes have exactly four descendants.

84. The split and merge procedure: Split into four disjoint quadrants any region Ri for which P(Ri) = FALSE. Merge any adjacent regions Rj and Rk for which P(RjURk) = TRUE. (the quadtree structure may not be preserved) Stop when no further merging or splitting is possible.

85. Motion-Based Segmentation Use motion as a cue to distinguish moving objects in an image sequence (video) Assumption: regions that moves are of interests than still backgrounds Successive image frames are taken from the same camera at the same shot. Spatial versus frequency domain methods

86. Accumulative Difference Image Difference Image

87. ADI Calculations Absolute, positive, and negative ADIs R(x,y): original image f(x,y,k) = f(x,y,tk) k-th frame in a sequence of images to be compared to R(x,y)

88. ADI: accumulative difference image

89. Example of Using ADI

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