Image enhancement

Antti Tuomas Jalava

Jaime Garrido Ceca

Overview

Digital subtraction angiography. Dual-energy and energy-subtraction X-ray imaging. Temporal subtraction.

Gray-scale transform. Convolution mask operators. High-frequency enhancement. Adaptive contrast enhancement. Objective assessment of Contrast Enhancement.

Digital Subtraction Angiography

PROCESS : Agent is injected to increase the density of the blood Number of X-ray images. An image taken before the injection of the agent is used as the

mask or reference image. Subtracted from the “live” images to obtain enhanced images. Useful to detect sclerosis. The mathematical procedure involved may be expressed simply as:

Sensitive to motion

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Dual-energy and Energy-subtraction X-ray Imaging

X-ray images at multiple energy levels Distribution of specific materials in the

object or body imaged Weighted combinations of multiple-energy

images soft-tissue and hard tissue separately

Temporal Subtraction

To detect normal or pathological changes occurred over a period of time.

Detection of lung nodules Normal anatomic structures are

suppressed and pathological are enhanced.

Gray Scale TransformOverview

Gray-scale thresholding. Gray-scale windowing. Gamma correction. Histogram transformation. Histogram specification. Limitation of global operations. Local-area histogram equalization. Adaptive-neighborhood histogram equalization.

Gray-scale Transforms (I)

Presence of different levels of density or intensity in the image.

Histogram gray-scale transform. Improve the visibility of details.

Gray-scale Transforms (II)

Gray-scale thresholding. Gray level object > L new bi-level image.

Problem: Narrow range of gray levels. Solution: Stretch the range of interest to the full range.

Gray-scale windowing. Linear transformation

Gamma correction. Non-linear transformations

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Thresholding

Original imageOriginal image New ImageNew ImageL = 30L = 30

Gamma Curve

Gamma Correction

Original imageOriginal image New imageNew imageγγ = 0.3 = 0.3

Windowing

Original imageOriginal image New imageNew imagef1 = 5 f2 = 60f1 = 5 f2 = 60

Histogram Transformation

Principle: maximal information is conveyed when PDF is uniform.

Histogram transformation is used to enhance the image.

Histogram-based methods: Histogram equalization. Histogram specification. Local-area histogram equalization (LAHE). Adaptive-neighborhood histogram equalization.

Histogram Equalization

Goal:

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Histogram Specification

Problem: H. Equalization provides only one output image. Not satisfactory in many cases.

Histogram Specification is a series of histogram-equalization steps to obtain prespecified histogram.

Process:

1. Specify the desired histogram and derive

2. Derive the histogram-equalizing transform

3. Derive from

4. Obtain

5. Transform to image f.

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Limitations of Global Operations

Global operators (Gray-scale & histogram transform) provides simple mechanisms to manipulate the image.

Global approach to image enhancement ignores the nonstationary nature of images.

Given wide range of details of interest in medical image, such as hard and soft tissues, it is desirable to design local and adaptive transform for effective image enhancement.

Local-area Histogram Equalization (LAHE)

Problem: Gray levels with low probability are merged upon quantization of the equalizing transform lost in the enhanced image.

2D sliding window. Resulting transform is applied only to the central pixel. Computationally expensive. LAHE variation:

Not every pixel. Only nonoverlapping rectangular block spanning the image.

Adaptive-neighborhood Histogram Equalization

Limitation of LAHE: no justification to the choice of the rectangular shape and the size of the window.

Identification of shape and size neighborhoods for each pixel by region growing.

Uniform region spans a limited range of gray levels by a specified threshold.

Local area composed not only by foreground region growing but also by background one.

Histogram of the local region equalizing transform to the seed pixel and all the pixels with the same value.

Adaptive-neighborhood Histogram Equalization

Original Equalization,Background depth 5,growth threshold 16

Convolution Mask Operators for Image Enhancement

2D convolution of images with 3 x 3 masks.

1. Unsharp masking

2. Subtraction Laplacian

Convolution Mask OperatorsUnsharp Masking Tackles blurring by an unknown phenomenon.

• Assumes that each pixel of original image contributes also to neighboring pixels.

Results into a fog.

Procedure:

1. The original degraded image is blurred.2. The blurred image is subtracted from the degraded

image. Removes the fog.

General form:

Where is local mean in degraded image .

Mean filter

Unsharp mask

Convolution Mask OperatorsSubtraction Laplacian Assumption that degraded image is a result of diffusion process that spreads

intensity values over space as a function of time

3 x 3 convolution mask formof Laplacian (gradient):

With weighting factor set to 1the subtraction Laplacian is:

Convolution Mask OperatorsProblems

Edge enhancement & high-frequency emphasis (Over and under-shoot seen as halos around edges). While seeming sharper, some finer details might be lost.

Can lead to negative pixel values.• Linear mapping back to display range can cancel any

enhancing.

Fixed operators.• No adaptivity to variability within image.

Original Unsharp mask,A = 1, B = 9,Normalized

dynamic range

Unsharp mask,A = 1, B = 9,

Dynamic range cut to original

Subtracting Laplacian,

A = 1, B = 5,Normalized

dynamic range

High-frequency Emphasis Bad idea: Ideal highpass filter

Introduces ringing artifacts.

Butterworth highpass filter Use of smooth transition from stopband to pass

band. Artifact reduction.

Extracts only edges. Order n.

Butterworth high-emphasis filter Adds constant to frequency space.

Preserves image and sharpens edges.

Homomorphic Filtering (I) Already known: Two images with different frequency composition that are added

together can be separated with linear filtering.

Two images multiplied with each other?

Take logarithm first.

(subscript l indicates that Fourier transform has been applied to Fourier transformed image)

Then filter, inverse Fourier transformand reverse logarithm with exponent.

Homomorphic Filtering (II)

Extension for convolved images (Chapter 10.3).→ generalized linear filtering.

Operations are called homomorphic systems.

With highpass filter used to achieve simultaneous dynamic range compression (brightness normalization) and contrast enhancement.

Original

Butterworth High-frequency emphasis filter,

n = 1, D = 0.6,Ka = 0.1,Kb = 0.5

Butterworth High-pass filter,

n = 1, D = 0.6

Homomorphic filtering

Butterworth High-frequency emphasis filter,

n = 1, D = 0.6,Ka = 0.1,Kb = 0.5

Adaptive-neighborhood Enhancement in General

Adaptive neighborhood (foreground): Interconnected segment of pixels with certain common property with a seed

pixel. (Found with seed fill.) Properly defined segments should correspond to image features.

Found regions are extended to overlap with adjacent regions (background). Borders of few pixels wide. Prevents edge artifacts like reversed intensity across border.

Enhancing algorithm is performed within the combined foreground and background. Result is applied to each seed pixel and each pixel within foreground with same

value of property than seed. Other pixels in foreground grow their own neighborhood.

Common property: Similar gray value To be exact: Growth tolerance .

If , all pixels connected to seed pixel with gray value between 0.95 and 1.05 times the seed pixel’s gray value are included to foreground.

→ All grown regions have contrast higher than independent of seed pixel’s gray value.

Worst case scenario

= average foreground pixel gray value

= average background pixel gray value Weber’s ratio of 2 % (for contrast of visible features)

should be about 4 %. Algorithm: Increase contrast to by replacing seed pixel’s value with

Adaptive-neighborhood Contrast Enhancement

(From equation 2.7)

(From equation 2.7)

OriginalAdaptive-

neighborhood contrast

enhancement,

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Objective Assessment of Contrast Enhancement

Contrast histogramDistribution of contrast of all possible regions

obtained by seed fill algorithm. Enhanced image should contain more counts of

regions at higher contrast levels. In practice same as more spread contrast histogram. The second moment is used to characterize the

spread

Image Enhancing- Ending Remarks

1. Better contrast2. sharpness of detail and3. visibility of features

are the targets for image enhancing.

Results can vary with each approach and image.

It can be beneficial to obtain several enhanced images with variety of approaches (as with most fields of image analysis).

Image restoration is presented in chapter 10. Image restoration: reversing the degradation when the exact

mathematical model of degradation is known.

Seed Fill - Foreground

Seed Fill - Background