Correcting Image Defects Chaiwoot Boonyasiriwat October 30, 2020 - - PowerPoint PPT Presentation

Chaiwoot Boonyasiriwat

October 30, 2020

Correcting Image Defects

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▪ “Most digital cameras detect color in RGB channels.” ▪ “An RGB color space is an additive color space based

• n the RGB color model.” (Wikipedia)

▪ “The RGB color model is simple because the axes are

• rthogonal.”

RGB Color Space

Russ and Neal (2016; p.164)

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▪ “CIE chromaticity diagram is a 2D plot defining color.” ▪ The third axis (pointing out of plane) is brightness. ▪ “Mixing any 2 colors corresponds to selecting a new point along a straight line between the 2 colors.” ▪ CRT monitor can produce colors shown in the triangle. ▪ The range of possible colors for any display is called gamut

CIE Chromaticity Diagram

Russ and Neal (2016; p.164)

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RGB can be transformed to CIEL*a*b* by where Xn, Yn, Zn are calculated using R = G = B = 100.

CIELab Color Space

Lightness from black (0) to white (100) From green to red From blue to yellow

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▪ “The CIE diagram provides a means for color definition but does not correspond directly to human vision.” ▪ To address this issue, HSV (hue, saturation, value), HSI (hue, saturation, intensity), and HLS (hue, lightness, saturation) coordinate systems were defined. ▪ “Hue is what people mean by color.” ▪ “Saturation is the amount of color that is present.” ▪ “The third axis (lightness, brightness, intensity, or value) is the amount of light.”

HSI Color Space

Russ and Neal (2016; p.166)

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HSI Color Space

Russ and Neal (2016; p.167)

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▪ Projecting a tilted RGB cube onto a plane yields a hexagon with red, yellow, green, cyan, blue, and magenta at its corner. ▪ “Hue is roughly the angle of the vector to a point in the projection.” ▪ Red at 0. Chroma C is the distance

• f the point from the origin.

HSI Color Space

Wikipedia

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▪ Hue can be computed by ▪ Lightness can be computed by

HSI Color Space

https://en.wikipedia.org/wiki/HSL_and_HSV

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▪ Smoothing can reduce random noise in an image. ▪ Smoothing can be performed by multiplying a portion

• f an image by an averaging kernel.

▪ Example: boldface number represents the center pixel ▪ This filter is applied at one location and is shifted to another location until all pixels in the image are processes so the filter is called a moving average filter.

Smoothing Filter

Russ and Neal (2016; p.180)

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▪ A Gaussian smoothing filter has a kernel that approximate the Gaussian function

Gaussian Smoothing

Russ and Neal (2016; p.181)

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▪ A 7x7 Gaussian smoothing kernel ▪ Instead of applying a 2D filter, we can apply two 1D filters in horizontal and vertical directions.

Gaussian Smoothing

Russ and Neal (2016; p.182)

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▪ Applying a filter is to convolve an image with the filter.

Gaussian Smoothing

Russ and Neal (2016; p.183)

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▪ A median filter can reduce noise with extreme values from an image by applying a median operation as a kernel.

Median Filter

Russ and Neal (2016; p.186)

5x5 median filter

Examples of kernel shapes

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▪ Nonuniform illumination in an image can be removed by image subtraction. ▪ Images A and B were recorded under the same lighting conditions.

Nonuniform Illumination

Russ and Neal (2016; p.216)

A - B = C

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▪ To enhance a fingerprint on a bank note, the complex background is removed by an image subtraction using an image of another note. ▪ Alignment between the two image was performed using cross-correlation.

Forensic Application

Russ and Neal (2016; p.216)

A - B = C

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▪ When the background image is not recorded, we may use interpolation to generate a background image.

Nonuniform Illumination

Russ and Neal (2016; p.218)

The red part was masked

• ut.

A third-order polynomial was used to fit the background points:

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▪ When the background is darker than foreground, we can subdivide the image into many regions. ▪ Within each region, we find the darkest pixel.

Nonuniform Illumination

Russ and Neal (2016; p.219)

These values and their locations are used to fit the polynomial and then subtract it from the original image.

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▪ If the features of interest are smaller than the background which is darker or lighter than the features, we can use rank operations such as median. ▪ In (b), each pixel is replaced by the darkest pixel in a 5x5 kernel. ▪ (c) is the result after 4 repetitions of this operation. ▪ a – c = d

Rank Leveling

Russ and Neal (2016; p.223)

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Rank Leveling

Russ and Neal (2016; p.225)

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Rank Leveling

Russ and Neal (2016; p.225)

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Rank Leveling on Color Image

Russ and Neal (2016; p.227)

▪ The background image is obtained by using a morphological opening operation.

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Geometric Distortion

Russ and Neal (2016; p.230)

▪ Geometric distortion in an image can be rectified by identifying 4 points on the image ▪ The real coordinates of these 4 points must be known. ▪ Substituting the coordinates of the 4 points and into the equations will lead to a linear system whose solution contains the values of ai and bi. ▪ The equations are then used to form all the pixels in the image.

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Geometric Distortion

Russ and Neal (2016; p.232)

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Geometric Distortion

Russ and Neal (2016; p.232)

▪ Combining 4 images after correcting the distortion enhances the license plate.

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Image Alignment

Russ and Neal (2016; p.234)

▪ Multiple images might need some alignment so that they can be patched together, e.g., as shown below. ▪ “Points to be aligned may be located manually by the user or automatically using cross-correlation.” ▪ Alignment equations are of the form

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Image Alignment

Russ and Neal (2016; p.230)

▪ Registration of PET (small), MRI (medium), and CT (large) images. 3 points are used for alignment.

▪ J. C. Russ and F. B. Neal, 2016, The Image Processing Handbook, 7th edition, CRC Press.

References