CIS 601 – 03 Image ENHANCEMENT SPATIAL DOMAIN Longin Jan Latecki in the SPATIAL DOMAIN Longin Jan Latecki Based on Slides by Dr. Rolf Lakaemper

Most of these slides base on the textbook Digital Image Processing by Gonzales/Woods Chapter 3

Image Enhancement ? Spatial Domain ? Introduction Image Enhancement ? Enhance otherwise hidden information Filter important image features Discard unimportant image features Spatial Domain ? Refers to the image plane (the ‘natural’ image) Direct image manipulation

A 2D grayvalue - image is a 2D -> 1D function, Remember ? A 2D grayvalue - image is a 2D -> 1D function, v = f(x,y)

As we have a function, we can apply operators to this function, e.g. Remember ? As we have a function, we can apply operators to this function, e.g. T(f(x,y)) = f(x,y) / 2 Operator Image (= function !)

T transforms the given image f(x,y) into another image g(x,y) Remember ? T transforms the given image f(x,y) into another image g(x,y) T f(x,y) g(x,y)

The operator T can be defined over Spatial Domain The operator T can be defined over The set of pixels (x,y) of the image The set of ‘neighborhoods’ N(x,y) of each pixel A set of images f1,f2,f3,…

Operation on the set of image-pixels Spatial Domain Operation on the set of image-pixels 6 8 2 3 4 1 12 200 20 10 6 100 10 5 (Operator: Div. by 2)

Operation on the set of ‘neighborhoods’ N(x,y) of each pixel Spatial Domain Operation on the set of ‘neighborhoods’ N(x,y) of each pixel 6 8 12 200 (Operator: sum) 6 8 2 226 12 200 20 10

Operation on a set of images f1,f2,… Spatial Domain Operation on a set of images f1,f2,… 6 8 2 12 200 20 10 11 13 3 (Operator: sum) 14 220 23 14 5 5 1 2 20 3 4

Operation on the set of image-pixels Spatial Domain Operation on the set of image-pixels Remark: these operations can also be seen as operations on the neighborhood of a pixel (x,y), by defining the neighborhood as the pixel itself. The easiest case of operators g(x,y) = T(f(x,y)) depends only on the value of f at (x,y) T is called a gray-level or intensity transformation function

Basic Gray Level Transformations Image Negatives Log Transformations Power Law Transformations Piecewise-Linear Transformation Functions For the following slides L denotes the max. possible gray value of the image, i.e. f(x,y)  [0,L]

Image Negatives: T(f)= L-f Transformations Image Negatives: T(f)= L-f T(f)=L-f Output gray level Input gray level

Transformations Log Transformations: T(f) = c * log (1+ f)

Transformations Log Transformations InvLog Log

Transformations Log Transformations

Power Law Transformations T(f) = c*f 

varying gamma () obtains family of possible transformation curves Transformations varying gamma () obtains family of possible transformation curves  > 1 Compresses dark values Expands bright values  < 1 Expands dark values Compresses bright values

Used for gamma-correction Transformations Used for gamma-correction

Used for general purpose contrast manipulation Transformations Used for general purpose contrast manipulation

Piecewise Linear Transformations

Thresholding Function Piecewise Linear Transformations Thresholding Function g(x,y) = L if f(x,y) > t, 0 else t = ‘threshold level’ Output gray level Input gray level

Purpose: Highlight a specific range of grayvalues Two approaches: Piecewise Linear Transformations Gray Level Slicing Purpose: Highlight a specific range of grayvalues Two approaches: Display high value for range of interest, low value else (‘discard background’) Display high value for range of interest, original value else (‘preserve background’)

Piecewise Linear Transformations Gray Level Slicing

Operation on a set of images f1,f2,… Operations on a set of images Operation on a set of images f1,f2,… 6 8 2 12 200 20 10 11 13 3 (Operator: sum) 14 220 23 14 5 5 1 2 20 3 4

Logic (Bitwise) Operations Operations on a set of images Logic (Bitwise) Operations AND OR NOT

The operators AND,OR,NOT are functionally complete: Operations on a set of images The operators AND,OR,NOT are functionally complete: Any logic operator can be implemented using only these 3 operators

Any logic operator can be implemented using only these 3 operators: Operations on a set of images Any logic operator can be implemented using only these 3 operators: A B Op 1 Op= NOT(A) AND NOT(B) OR NOT(A) AND B

Image 1 AND Image 2 Operations on a set of images 1 2 3 9 7 3 6 4 1 1 1 1 (Operator: AND) 2 2 2 1 1 1 1 2 2 2 2

Used for Bitplane-Slicing and Operations on a set of images Image 1 AND Image 2: Used for Bitplane-Slicing and Masking

Operations on a set of images Exercise: Define the mask-image, that transforms image1 into image2 using the OR operand 1 2 3 9 7 3 6 4 255 2 7 255 (Operator: OR) 255 3 7 255

Arithmetic Operations on a set of images 1 2 3 9 7 3 6 4 2 3 4 10 (Operator: +) 9 5 8 6 1 1 1 1 2 2 2 2

What could the operators + and – be used for ? Operations Exercise: What could the operators + and – be used for ?

Foreground-Extraction Operations Example: Operator – Foreground-Extraction

Operations Example: Operator + Image Averaging