Contrast Enhancement Yao Wang Polytechnic University University, Brooklyn Brooklyn, NY 11201 With contribution from Zhu Liu, Onur Guleryuz, and Gonzalez/Woods, Digital Image Processing, 2ed
Lecture Outline • • • • • •
Introduction Linear stretching Nonlinear stretching Histogram equalization Histogram specification Adaptive histogram modification
Yao Wang, NYU-Poly
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What is Contrast Enhancement
Original image with low contrast
Yao Wang, NYU-Poly
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Enhanced image
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How to enhance the contrast
• Low contrast image g values concentrated near a narrow range (mostly dark, or mostly bright, or mostly medium values) • Contrast enhancement change the image value distribution to cover a wide range • Contrast of an image can be revealed by its histogram
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Histogram • Histogram of a monochrome image with L possible gray levels levels, f = 0 0, 1 1, …, L-1 L-1. – P(l) = nl / n, • nl is the number of pixels with gray level ll. • n is the total number of pixels in the image.
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Histogram Calculation function h = histogram(imgname) img = imread(imgname); figure; imshow(img); % method 1 h = zeros(256,1); for l = 0:255 for i = 1:N, for j = 1:M, if img(i, j) == l, h(l + 1) = h(l + 1) + 1 1; end end end end figure; bar(h);
% method 2 img = double(img); h = zeros(256 zeros(256,1); 1); for i=1:M, for j=1:N, f = img(i,j); h(f+1) = h(f+1) + 1; end end % method 3 h = zeros(256,1); for l = 0 : 255, h(l + 1) 1)=sum(sum(img ( (i == l)) l)); end
Photoshop otos op has as e extensive te s e histogram stog a d display sp ay too tools s Matlab: imhist( ): can compute and display histograms Yao Wang, NYU-Poly
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Histogram vs vs. Image Contrast
Images with figure captions in this and other slides are from [Gonzalez02]
Examples of Histograms p(f)
p(f)
p(f)
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(a) Too dark Yao Wang, NYU-Poly
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(b) Too bright EL5123: Contrast Enhancement
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(c) Well balanced 8
Very Different Images May Have Same Histogram!
Histogram reflects the pixel intensity distribution, not the spatial distribution! Yao Wang, NYU-Poly
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Previous Example
Original image with low contrast
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Enhanced image
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Histograms of Example Images 1600
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Original girl image with low contrast
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Enhancement image with histogram equalization
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How to change the histogram? Using g Point-Wise Transformation • Use a “function” g(f) to generate a new image B from a given image A via: B (i, j ) g ( A(i, j )), i 0,..., N 1, j 0,..., M 1
• The function g(f) operates on each image pixel independently All pixels with original gray level f independently. are changed to have gray level g(f) • Properties that g(f) should satisfy –M Monotonically i ll non-decreasing, d i so that h relative l i brightness of pixels do not change. – G(f) in the same range as original f, i.e. with same min ( (e.g. 0) and d max values l ((e.g. 255) 255), and db be iintegers t for digital images. • Rounding/truncation may be needed
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How to Determine the Transformation Function? • How to design the transformation function g(f)? – depends on the histogram of the original image hA(f) and the desired histogram of the transformed image hB(f). – To enhance contrast, we like hB(f) to be as flat as possible.
• Different approaches – Using fixed functional forms: linear, non-linear – Using adaptive transform, that is determined from hA(f) and hB(f): • Histogram equalitzation (hB(f) is uniform): Fully automatic! • Histogram specification or matching
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Linear Stretching • Enhance the dynamic range by linearly stretching the original gray levels to the range of g(f) af b 0g (tof )255. t s1 s2 t1 t2 2
g ( f ) ( f s1 ) * (t 2 t1 ) /( s2 s1 ) t1 a (t 2 t1 ) /( s2 s1 ), b t1 s1 * (t 2 t1 ) /( s2 s1 )
s1
• Example – – –
t1
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The original g g gray y levels are [[100,, 150]. ] The target gray levels are [0, 255]. The g ( f transformation ) (( f 100) /function 50) * 255, ffor 100 f 150.
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Illustration of Linear Stretching p(f)
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Linear stretching
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Piecewise Linear Stretching • K segments – Starting position of input {fk, k = 0, 0 …K K-1} 1} – Starting position of output {gk, k = 0, …, K-1} g – Transform T f function f ti f fk g( f ) * ( g k 1 g k ) g k ; f k 1 f k for f k f f k 1 , k 0,1,..., K 1.
g4 g3
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Piece-Wise Linear for Middle Range Image
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Special Cases • Thresholding (slicing) g0 g( f ) g1
f T f T
• Multilevel Slicing g( f ) gk
f k f f k 1
g(f) g1 g0 f
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g(f) g2 g1 g0 f0
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• The mapping function should be monotonically non-decreasing, so that the relative brightness orders of pixels do not change Yao Wang, NYU-Poly
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Nonlinear Stretching • • • •
Nonlinear functions with a fixed form Fewer parameters to adjust Satisfying 0 f min g f max L 1 Examples – Logarithmic transformation
g b log(af 1)
• Stretch dark region, g , suppress pp bright g region g
– Exponential transformation • Expand bright region
– Power Law
g b(e af 1) g aff
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• K = 2: square law, similar to exponential • K = 1/3: /3 cub cubic c root, oot, ssimilar a to logarithmic oga t c
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Enhancement of Too-Dark Images
H(f) g gmax
New histogram
fmax H(g) Original histogram fmax
Transformation function: “log” function: g=c log (1+f) Or Power law: g= c f^r, 0adjustments >adjustments • Try brightness/contrast, curves, equalize
• Matlab – Imhist, histeq, imadjust, imcontrast – imadjdemo i djd
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Summary • What is image histogram? • How Ho to tell whether hether an an image ha have ea good contrast from its histogram? • Given the histogram of an image, can you sketch a transformation that will likely improve the image contrast. • The principle of histogram equalization • The principle of histogram specification • Color image enhancement Yao Wang, NYU-Poly
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Homework 1.
Following figure shows the histogram of an image and two transformation functions. Sketch the histograms of the images obtained by applying the two functions to the original image. g2(f) 255 h(f) g1(f) 128 a 128 0
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Following figure (next slide) shows the histograms of three different images, and three possible point functions. For each original image, which p point operation p can best equalize q its histogram? g Briefly y explain p your reasoning.
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Homework (cntd) 3.
For the histogram h3(f) given in the following figure, determine analytically the histogram equalizing function, assuming the dynamic range of the signal f is from 0 to 1 (i.e. replacing 128 by ½, 255 by 1). The two 8-level 8 level images have histograms hA=[.1, =[ 1 .2, 2 .3, 3 0 0, .1, 1 0 0, 0 0, .3], 3] hB=[.1, 0, .2, 0, .4, 0, .3, 0]. Find a point function g(f) that when operating on image A will produce an image C that has a histogram that is similar to hB.
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0 64 Yao Wang, NYU-Poly
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Computer Assignment 1.
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Write a Matlab function that can compute the histogram of a grayscale image (assuming 256 levels of gray). Try the three possible ways described in slide 7, and see which one is faster. Finalize your program with the fastest method. method In a separate main program, program apply the program to a test image, and display the histogram as a stem plot besides the image (using “subplot” function). You are not allowed to simply use the “imhist” or “hist” function in Matlab, although you are encouraged to compare p yyour results with those obtained using g these functions. Write a Matlab program that performs histogram equalization on a grayscale image. Your program should: i) compute the histogram of the input image; ii) compute the histogram equalizing transformation function; iii) apply the function to the input image; iv) compute the histogram of the equalized li d iimage; v)) di display l ((and d print) i t) th the original i i l and d equalized li d iimages, as well as their corresponding histograms, all in one figure. You are not allowed to simply use the “histeq” function in Matlab, although you are encouraged to compare your results with those obtained using these functions. functions Play with the “imadjdemo” program in Matlab, to see the effect of different choice of the transformation functions on image contrast and brightness. Write down your observations in your report.
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Readings • Gonzalez & Woods, “Digital Image Processing”, Chapter 3 (Section 3.1 – 3.3) • Jain, “Fundamentals of Digital Image Processing”, g , Chapter p 7 ((Section 7.1 – 7.3))
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