Chapter 3 Image Enhancement Image Enhancement The principal

Chapter 3 Image Enhancement

Image Enhancement The principal objective of enhancement is to process an image so that the result is more suitable than the original image for a specific application The specific application may determine approaches or techniques for image enhancement Image enhancement approaches fall into two broad categories Spatial domain methods Frequency domain methods

Spatial Domain Methods • Procedures that operate directly on pixels. g(x, y) = T[f(x, y)] where – f(x, y) is the input image – g(x, y) is the processed image – T is an operator on f defined over some neighborhood of (x, y)

Spatial Domain Methods (x, y) • • Neighborhood of a point (x, y) can be defined by using a square/rectangular (common used) or circular subimage area centered at (x, y) • The center of the subimage is moved from pixel to pixel starting at the top of the corner

Spatial Domain Methods The smallest possible neighborhood is of size 1 x 1 s=T(r) ; gray-level transformation s, r : gray level

Gray Level Transformations

Image Negatives Image in the range [0, L-1] It is useful in displaying medical images

Image Negatives

Log Transformations s = c log(1+r) c : constant, r >= 0 We use a transformation of this type to expand the values of dark pixels while compressing the higher-level values The opposite is true of the inverse log transformation

Power-Law Transformations s = cr • c and are positive constants • Power-law curves with fractional values of map a narrow range of dark input values into a wider range of output values, with the opposite being true for higher values of input levels. • c = = 1 Identity function

Power-Law Transformations Cathode ray tub (CRT) devices have intensity-tovoltage response that is a power function Exp. varies approximately 1. 8 to 2. 5 tends to produce darker images (from the graph)

Power-Law Transformations

Power-Law Transformations

Power-Law Transformations

Piecewise-Linear Transformation Functions • Advantage: – The form of piecewise functions can be arbitrarily complex • Disadvantage: – Their specification requires considerably more user input

Contrast-stretching • If r 1=s 1 and r 2=s 2, linear function produces no changes in gray levels. • If r 1=r 2, s 1=0 and s 2=L-1, thresholding • creates a binary image • Intermediate values of (r 1, s 1)and (r 2, s 2) various degrees of spread in the gray levels of the output image, thus affecting its contrast.

Contrast-stretching • increase the dynamic range of the gray levels in the image • (b) a low-contrast image • (c) result of contrast stretching: (r 1, s 1) = (rmin, 0) and (r 2, s 2) = (rmax, L-1) • (d) result of thresholding

Intensity-Level Slicing • Highlighting a specific range of gray levels in an image – Display a high value of all gray levels in the range of interest and a low value for all other gray levels • (a) transformation highlights range [A, B] of gray level and reduces all others to a constant level • (b) transformation highlights range [A, B] but preserves all other levels

Intensity-Level Slicing

Bit-Plane Slicing Highlighting the contribution made to total image appearance by specific bits

Bit-Plane Slicing

Bit-Plane Slicing Decomposing an image into its planes is useful for analyzing the relative importance of each bit. Determine the number of bits adequate to quantize the image Reconstructing of an image is done by multiplying the pixels in nth plane by the constant 2 n-1.

Histogram Processing • Histogram of a digital image with gray levels in the range [0, L-1] is a discrete function • h(rk) = nk • Where – rk : the kth gray level – nk : the number of pixels in the image having gray level rk – h(rk) : histogram of a digital image with gray levels rk - p(rk) = nk/MN , k=0, 1, …, L-1 - p(rk) is an estimate of the probability of occurrence of gray level k

Histogram Processing

Histogram Processing

Histogram Equalization Consider a transformation such as s= T(r), 0 ≤ r ≤ L-1 Assume T(r) satisfies the following conditions (a) T(r) is a monotonically increasing in the interval 0 ≤ r ≤ L-1; (b) 0 ≤ T(r) ≤ 1 for 0 ≤ r ≤ L-1 Monotonically preserves the increasing order from black to white in the image Condition b guarantees that the output gray level will be in the same range as input. Single valued is required to guarantee the inverse transformation will exist r =T-1(s) 0≤ s ≤L-1 To achieve this, T(r) is a strictly monotonically increasing function in the interval 0 ≤r ≤L-1

Histogram Equalization

Histogram Equalization • Let – pr(r) denote the PDF of random variable r – ps (s) denote the PDF of random variable s • If pr(r) and T(r) are known and T-1(s) satisfies condition (a) then ps(s) can be obtained using a formula : n A transformation function is :

Histogram Equalization

Histogram Equalization

Histogram Equalization • The probability of occurrence of gray level in an image is approximated by • The discrete version of transformation =

Histogram Equalization A 3 -bit image 0 f size 64× 64 pixels (MN =4096) has the intensity distribution shown in the table.

Histogram Equalization

Histogram Equalization

Histogram Equalization