EE 4780

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EE 4780. Image Enhancement. Image Enhancement. The objective of image enhancement is to process an image so that the result is more suitable than the original image for a specific application. There are two main approaches:

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EE 4780

Image Enhancement

Image Enhancement
• The objective of image enhancement is to process an image so that the result is more suitable than the original image for a specific application.
• There are two main approaches:
• Image enhancement in spatial domain: Direct manipulation of pixels in an image
• Point processing: Change pixel intensities
• Spatial filtering
• Image enhancement in frequency domain: Modifying the Fourier transform of an image
Image Enhancement by Point Processing
• Intensity Transformation

Matlab exercise

Histogram Specification
• Intensity mapping
• Assume
• T(r) is single-valued and monotonically increasing.
• The original and transformed intensities can be characterized by their probability density functions (PDFs)
Histogram Specification
• The relationship between the PDFs is
• Consider the mapping

Cumulative distribution function of r

Histogram equalization!

Image Enhancement by Point Processing
• Histogram Equalization Example

Intensity 0 1 2 3 4 5 6 7

Number of pixels 10 20 12 8 0 0 0 0

Intensity 0 1 2 3 4 5 6 7

Number of pixels 0 10 0 0 20 0 12 8

Local Histogram Processing
• Histogram processing can be applied locally.
Image Subtraction

The background is subtracted out, the arteries appear bright.

Image Averaging

Corrupted

image

Original

image

Noise

Assume n(x,y) a white noise with mean=0, and variance

If we have a set of noisy images

The noise variance in the average image is

Spatial Filtering

A low-pass filter

A high-pass filter

Spatial Filtering
• Median Filter

Sort: (10 10 10 20 25 75 85 90 100)

• Example

Original signal:

100 100 100 100 10 10 10 10 10

Noisy signal:

100 103 100 100 10 9 10 11 10

Filter by [ 1 1 1]/3:

101 101 70 40 10 10 10

Filter by 1x3 median filter:

100 100 100 10 10 10 10

Spatial Filtering
• Median filters are nonlinear.
• Median filtering reduces noise without blurring edges and other sharp details.
• Median filtering is particularly effective when the noise pattern consists of strong, spike-like components. (Salt-and-pepper noise.)
Spatial Filtering

Original

3x3 averaging filter

3x3 median filter

Wiener Filter

Noisy

image

Original

image

Noise

Wiener Filter

Signal variance

Noise variance

Wiener Filter

is estimated by

Since variance is nonnegative, it is modified as

Estimate signal variance locally:

N

N

Wiener Filter

Denoised (3x3neighborhood)

Mean Squared Error is 56

Noisy, =10

wiener2 in Matlab

Spatial Filtering
• High-boost or high-frequency-emphasis filter
• Sharpens the image but does not remove the low-frequency components unlike high-pass filtering
Spatial Filtering
• High-boost or high-frequency-emphasis filter
• High pass = Original – Low pass
• High boost = (Original) + K*(High pass)
Spatial Filtering

A high-pass filter

A high-boost filter

Spatial Filtering
• High-boost or high-frequency-emphasis filter