Chapter 3Image Enhancement in the Spatial Domain

Outline Background Basic Gray-level transformation Histogram Processing Arithmetic-Logic Operation Basics of Spatial Filtering Smoothing Spatial Filters Sharpening Spatial Filters Combining Spatial Enhancement Methods

Image enhancement approaches fall into two broad categories: spatial domain methods and frequency domain methods.

The term spatial domain refers to the image plane itself.

g(x,y)= T[f(x,y)] , T is an operator on f, defined over some neighborhood of f(x,y)

Background

Size of Neighborhood Point processing Larger neighborhood: mask (kernel,

template, window) processing

Gray-level Transformation

Contrast stretching thresholding

Basic Gray Level Transformation

Image negatives: s =L-1-r Log transformation: s =clog(1+r) Power-law transformation: s=cr

Image Negatives

Log Transformation

Gamma Correction (I) Cathode ray tube (CRT) devices have an

intensity-to-voltage response that is a power function, with exponents varying from 1.8 to 2.5.

Gamma Correction (II)

Piece-wise Linear Transformation Contrast stretching Gray-level slicing

(Figure 3.11) Bit-plane slicing

(Figures 3.13-14)

Gray-level Slicing

Bit-plane Slicing

Histogram Processing The histogram of a digital image with gray-levels in the range [0,L-1] is a discrete function h(rk)=nk where rk is the kth gray level and nk is the number of pixels in the image having gray level rk Normalized histogram: p(rk)=nk/n. Easy to compute, good for real-time image processing.

Four Basic Image Types

Histogram Equalization s= T(r) What if we take the transformation T to be: It can be shown that ps(s)=1 Discrete version:

Histogram Matching

Local Enhancements

Histogram Statistics N-th moment of r about its mean:

Logic Operations

Arithmetic Operations Image Subtraction Image Averaging

Basics of Spatial Filtering

•Mask, convolution kernels•Odd sizes

Smoothing Spatial Filters Smoothing linear filters: averaging filters,

low-pass filters Box filter Weighted average

Order-statistics filters: Median-filter: removing salt-and-pepper noise Max filter Min filter

Sharpening Spatial Filters Foundation:

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Image Enhancement

The Gradient

Simplification

Combining Spatial Enhancement Methods

(a) original (b) Laplacian, (c) a+b, (d) Sobel of (a)

(a) (b) (c) (d)