Image Enhancement in the Spatial Domain Chaiwoot Boonyasiriwat November 6, 2020
Image Histogram ▪ “Image histogram is a plot of the number of pixels with each possible brightness level.” ▪ “The visibility of structures can be improved by stretching the contrast so that the value of pixels are reassigned to cover the entire available range.” 2 Russ and Neal (2016, p. 245)
Contrast Expansion The linear mapping was applied to the original image (left) and provided a higher-contrast image (right). 3 Russ and Neal (2016, p. 246)
Contrast Expansion for Color Images ▪ Convert RGB to HSI or Lab color space. ▪ Apply the linear mapping to intensity, luminance, or lightness scale while leaving the color information unchanged. Original image expanding only intensity expanding RGB values Color shift occurs 4 Russ and Neal (2016, p. 248)
Contrast Manipulation ▪ The stored value of brightness of each pixel can be mapped to a displayed value using a transfer function. Red line is the transfer function. Displayed value Stored value 5 Russ and Neal (2016, p. 250)
Contrast Manipulation ▪ Gamma correction uses a nonlinear transfer function 1 1 6 Russ and Neal (2016, p. 252)
Contrast Manipulation ▪ “A transfer function can be created arbitrarily to reveal important details of an image.” 7 Russ and Neal (2016, p. 252-253)
Histogram Equalization ▪ Histogram equalization uses the cumulative curve (summation of pixel values) as the transfer function. ▪ The result uses all available brightness values equally. T is the total number of pixels. j is brightness level. N i is the number of Image after Original image pixels at brightness Histogram equalization level i . 8 Red line is the cumulative curve Russ and Neal (2016, p. 253)
Histogram Equalization 9 Russ and Neal (2016, p. 254)
Histogram Equalization 10 Russ and Neal (2016, p. 255)
Histogram Equalization for Color Image ▪ Convert RGB to HSI and apply histogram equalization to intensity only. Leave color information unchanged. 11 Russ and Neal (2016, p. 257)
Histogram Equalization for Color Image 12 Russ and Neal (2016, p. 258)
Local Equalization ▪ Histogram modification of local image regions can improve the visibility of some feature in an image. Images after local equalization Radius = 6 Radius = 3 Original image 13 Russ and Neal (2016, p. 257)
Variance Equalization ▪ Variance equalization also uses a moving neighborhood filter like local equalization ▪ Variance equalization only modifies the central pixel while local equalization modifies all pixels within the filtering region. ▪ “Statistical variance of the pixels in the region is computed and compared to that of the entire image, and the pixel values are adjusted to match the local variance to the global.” 14 Russ and Neal (2016, p. 257)
Variance Equalization (a) original. (b) local brightness equalization. (c) blend of (a) and (b) (d) local variance equalization 15 Russ and Neal (2016, p. 260)
Variance Equalization for Color Image Convert RGB to HSI and apply variance equalization to intensity only. Original Variance equalization with radius = 6 16 Russ and Neal (2016, p. 261)
Variance Equalization for Color Image Median filter (radius = 2) + variance equalization 2/3 of (b) + 1/3 of (c) 17 Russ and Neal (2016, p. 261)
Laplacian Sharpening ▪ Laplacian sharpening is a filter that enhance edges. ▪ The convolution kernel of a 3x3 Laplacian filter is It is an approximation to the Laplacian operator Original image Local equalization Laplacian 18 Russ and Neal (2016, p. 261)
Laplacian Sharpening SEM image of alumina Laplacian Sharpening operator fracture surface The convolution kernel of a sharpening operator is 19 Russ and Neal (2016, p. 263)
Unsharp Mask (a) Image of M101 (b) Out-of-focus negative of (a) (c) Combine (a) and (b) (d) Add (a) and (c) produces the (a) (b) unsharp mask result (c) (d) 20 Russ and Neal (2016, p. 269)
Unsharp Mask (a) (c) (b) (d) (a) Original image (b) Gaussian smoothed (c) (a) – (b) (d) (a) + (c) 21 Russ and Neal (2016, p. 270)
Unsharp Mask 22 Russ and Neal (2016, p. 270)
Difference of Gaussians (DoG) ▪ Subtract one smoothed version of the image from another having a different degree of smoothing. 23 Russ and Neal (2016, p. 271)
Difference of Gaussians (DoG) (a) Original image (b) 3x3 sharpening filter (c) DoG using = 0.5 and = 2.5 pixels 24 Russ and Neal (2016, p. 271)
Derivative ▪ Derivative filters are suitable for images having features with a principal orientation. (a) Chromatography in which proteins are spread along lanes in an electric field. (b) horizontal derivative using a 1-pixel high kernel. (c) horizontal derivative using a 5- pixel high kernel for noise reduction. 25
Derivative ▪ Typical kernels for horizontal first derivative are ▪ Kernels for first derivative in tilted direction 26
Derivative 3x3 derivative 3x3 Laplacian 3x3 sharpening 27
Derivative 28
Edge Detectors ▪ Edges of features are represented as a step in brightness ▪ “Laplacian filter, based on second derivative, gives a larger response to a line than to a step, and to a point than to a line.” ▪ “Directional first derivative only highlights edges in a direction perpendicular to their orientation.” ▪ One of earliest filters to locate edges of arbitrary orientation is the Roberts’ cross operator – applications of two first derivatives of brightness in perpendicular directions: 29
Edge Detectors ▪ A common method to combine two orthogonal vectors is to compute the magnitude of the resulting vector. ▪ An example is the Sobel gradient operator which is magnitude of the local gradient of brightness B : 30
Edge Detectors Absolute value of Original Horizontal derivative horizontal derivative Vertical derivative Absolute value of vertical derivative Sobel operator 31
Directional Derivative Filters 32
Edge Detectors Original 3x3 Sobel filter 7x7 Sobel filter 33
Edge Orientation ▪ The direction of the gradient vector can be computed by Gradient vector Gradient Assign gradient Assign gradient Original magnitude angle to magnitude to brightness intensity and direction to hue 34
Edge Orientation Sobel direction operator SEM image of Rose diagram eggshell membrane of fiber orientations 35
More Edge Detectors 36
References ▪ J. C. Russ and F. B. Neal, 2016, The Image Processing Handbook, 7 th edition, CRC Press.
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