EE 7730: Lecture 1 - LSU

EE 7730: Lecture 1 - LSU

EE 4780 Image Enhancement Image Enhancement The objective of image enhancement is to process an image so that the result is more suitable than the original image for a specific application. There are two main approaches: Image enhancement in spatial domain: Direct manipulation of pixels in an image

Point processing: Change pixel intensities Spatial filtering Image enhancement in frequency domain: Modifying the Fourier transform of an image Bahadir K. Gunturk 2 Image Enhancement by Point Processing Intensity Transformation Bahadir K. Gunturk

3 Image Enhancement by Point Processing Contrast Stretching Bahadir K. Gunturk 4 Image Enhancement by Point Processing Contrast Stretching T ( r ) c log(1 r ) Bahadir K. Gunturk 5

Image Enhancement by Point Processing Intensity Transformation Matlab exercise Bahadir K. Gunturk 6 Image Enhancement by Point Processing Intensity Transformation Bahadir K. Gunturk

7 Image Enhancement by Point Processing Intensity Transformation Bahadir K. Gunturk 8 Image Enhancement by Point Processing Gray-Level Slicing Bahadir K. Gunturk 9

Image Enhancement by Point Processing Histogram Number of pixels with intensity r p( r ) Total number of pixels p(r ) 0 Bahadir K. Gunturk r 255

10 Histogram Specification Intensity mapping s T (r ) Assume T(r) is single-valued and monotonically increasing. 0 T (r ) 1 and 0 r 1

The original and transformed intensities can be characterized by their probability density functions (PDFs) pr ( r ) ps ( s ) Bahadir K. Gunturk 11 Histogram Specification The relationship between the PDFs is p (s)ds p (r )dr 1 s

r dr p s ( s ) p r ( r ) ds r T 1 ( s ) Consider the mapping r s T (r ) p (w)dw r Cumulative distribution function of r w 0

r ds d pr ( w)dw pr (r ) dr dr w0 1 p s ( s ) pr ( r ) 1, pr (r ) r T 1 ( s ) Bahadir K. Gunturk 0 s 1 Histogram equalization!

12 Image Enhancement by Point Processing Histogram Equalization Number of pixels with intensity i r T (r ) round 255 Total number of pixels r Number of pixels with intensity i round 255

Total number of pixels i 0 r round 255 p(i ) i 0 0 r 255 Bahadir K. Gunturk

13 Image Enhancement by Point Processing Histogram Equalization Example Intensity Number of pixels 0 1 2 3 10 20 12 8 4 0 5 0

6 0 7 0 p(0) 10 / 50 0.2 p (1) 20 / 50 0.4 p (2) 12 / 50 0.24 p (3) 8 / 50 0.16 p(r ) 0 / 50 0, r 4,5, 6, 7 r T ( r ) round 7 p (i ) i 0 T (0) round 7 * p(0) round 7 *0.2 1 T (1) round 7 * p(0) p(1) round 7*0.6 4 T (2) round 7 * p(0) p(1) p(2) round 7 *0.84 6

T (3) round 7 * p(0) p(1) p(2) p(3) 7 T (r ) 7, r 4,5, 6, 7 Intensity Number of pixels Bahadir K. Gunturk 0 1 2 0 10 0 3 4 5 6 0 20 0 12 7 8 14 Image Enhancement by Point Processing

Histogram Equalization Bahadir K. Gunturk 15 Local Histogram Processing Histogram processing can be applied locally. Bahadir K. Gunturk 20 Image Subtraction g ( x, y ) f ( x, y ) h ( x, y ) The background is subtracted out, the arteries appear bright.

Bahadir K. Gunturk 21 Image Averaging g ( x, y ) f ( x, y ) n ( x, y ) Corrupted image Original image Noise 2

2 Assume n(x,y) a white noise with mean=0, and variance E n ( x, y ) If we have a set of noisy images gi ( x, y ) 1 The noise variance in the average image g ave ( x, y ) M 1 E M Bahadir K. Gunturk M n (

x , y ) i i 1 2 1 2 M

M 2 E n i ( x, y) i 1 M g ( x, y ) i is i 1

1 2 M 22 Image Averaging Bahadir K. Gunturk 23 Spatial Filtering 1 1 1 1 1 1 1

9 1 1 1 1 1 1 1 8 1 1 1 1 Bahadir K. Gunturk A low-pass filter A high-pass filter 24 Spatial Filtering Median Filter

10 20 10 25 10 75 90 85 100 Sort: (10 10 10 20 25 75 85 90 100) Example Original signal: 100 100 100 100 10 10 10 10 10 Noisy signal: 100 103 100 100 10 9 10 11 10 Filter by [ 1 1 1]/3: 101 101 70 40 10 10 10

Filter by 1x3 median filter: 100 100 100 10 10 10 10 Bahadir K. Gunturk 25 Spatial Filtering Median filters are nonlinear. Median filtering reduces noise without blurring edges and other sharp details. Median filtering is particularly effective when the noise pattern consists of strong, spike-like components. (Salt-andpepper noise.)

Bahadir K. Gunturk 26 Spatial Filtering Original 3x3 averaging filter Bahadir K. Gunturk Salt&Pepper noise added 3x3 median filter

27 Spatial Filtering Bahadir K. Gunturk 28 Wiener Filter Y X W Noisy image Original image Wiener Filter Noise

2 x X 2 Y 2 x w Signal variance Bahadir K. Gunturk Noise variance 29 Wiener Filter x2

is estimated by x2 y 2 w2 Since variance is nonnegative, it is modified as x2 max[0, y 2 w2 ] Estimate signal variance locally: x2 max[0, Bahadir K. Gunturk 1 N2 2 2 y

i w] i N N 30 Wiener Filter Noisy, =10 Denoised (3x3neighborhood) Mean Squared Error is 56 wiener2 in Matlab Bahadir K. Gunturk 31

Spatial Filtering 1 1 1 1 8 1 1 1 1 Bahadir K. Gunturk 35 Spatial Filtering High-boost or high-frequency-emphasis filter Sharpens the image but does not remove the low-frequency components unlike high-pass filtering

Bahadir K. Gunturk 36 Spatial Filtering High-boost or high-frequency-emphasis filter High pass = Original Low pass High boost = (Original) + K*(High pass) Bahadir K. Gunturk 37

Spatial Filtering 1 1 1 1 8 1 1 1 1 1 1 1 1 9 1 1 1 1 A high-pass filter A high-boost filter Bahadir K. Gunturk

38 Spatial Filtering High-boost or high-frequency-emphasis filter Bahadir K. Gunturk 39 Spatial Filtering Bahadir K. Gunturk 40

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