Chapter 3 Image 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 stretchingthresholding

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 )

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(r k )=n k where r k is the kth gray level and n k is the number of pixels in the image having gray level r k Normalized histogram: p(r k )=n k /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 p s (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:

The Laplacian Development of the method:

Image Enhancement

The Gradient Simplification

Combining Spatial Enhancement Methods (a) original (b) Laplacian, (c) a+b, (d) Sobel of (a) (a)(b)(c)(d)