An Extensive Empirical Evaluation of Focus Measures for Digital Photography Hashim Mir, Peter Xu, and Peter van Beek University of Waterloo
Dec 27, 2015
An Extensive Empirical Evaluation of Focus Measures for Digital Photography
Hashim Mir, Peter Xu, and Peter van BeekUniversity of Waterloo
• Digital cameras are equipped with contrast-based autofocus
• Contrast-detection autofocus makes use of a focus measure• maps an image to a value that represents degree of focus
of image
• Speed and accuracy of autofocus crucial to user satisfaction• search for an image with maximal focus according to focus
measure• choice of focus measure is an important factor in
performance of autofocus
February 4, 2014 Focus Measures for Digital Photography 2
Introduction
• Previous studies on focus measures:• small number of benchmarks images in their evaluation,• directed at microscopy and not digital cameras, or• based on ad hoc evaluation criteria
• Here: • extensive empirical evaluation of focus measures for digital
photography• advocate using three standard statistical measures of
performance—precision, recall, and mean absolute error—as evaluation criteria
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Introduction
• Introduction• Focus Measures• Related Work• Experimental Methodology• Experimental Results• Conclusion
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Outline
• Many focus measures have been proposed in the literature
• Let f (x, y) be the luminance or grayscale at pixel (x, y) in an image of size M × N pixels
• Example: squared gradient focus measure for an image acquired when the lens is at position p is given by,
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Focus measures
1 22
=0 =0
( ) = ( ( , 1) ( , ))M N
x y
p f x y f x y
(a) Focus measures of images at each lens position; (b) flower in focus
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(a) (b)
(a) Focus measures of images at each lens position; (b) fern & grasses in focus
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(a) (b)
• We evaluated more than 30 focus measures in our study
• The focus measures can be classified under six types:1. first-order differentiation2. second-order differentiation3. image histogram4. image statistics5. correlation6. data compression
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Focus measures: Categorizing
• Example: squared gradient• Example: focus measure based on 3×3 Sobel
operators,
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Focus measures: First-order differentiation
1 0 1 1 2 1
2 0 2 0 0 0
1 0 1 1 2 1
(horizontal) (vertical)
• Example: focus measure based on 3×3 Laplacian operator,
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Focus measures: Second-order differentiation
1 1 1
1 8 1
1 1 1
• Example: variance focus measure is given by,
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Focus measures: Image statistics
1 12
=0 =0
1( ) = ( ( , ) )
M N
x y
p f x yMN
where µ is the mean luminance of the image
• Example: Vollath’s F4 focus measure is given by,
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Focus measures: Correlation
2 1
=0 =0
31 1
=0 =0
( ) = ( , ) ( 1, )
( , ) ( 2, )
M N
x y
M N
x y
p f x y f x y
f x y f x y
February 4, 2014 Focus Measures for Digital Photography 13
Related work: Evaluating focus measures
setting citation conclusions
Microscopy applications
Groen, Young & Ligthart, 1985
squared gradient
Firestone et al. 1991 vertical Brenner, variance
Santos et al. 1997 Vollath's F4, F5
Liu, Wang & Sun 2007 variance
Digital photography
Subbarao and Tyan 1998 Laplacian
Ng, Neow & Ang 2001 first-order 3×3 Sobel, variance
Shih 2007 first-order 3×3 Sobel & Prewitt
Yousefi et al. 2011 Vollath's F4
• Step 1: Implemented a camera remote control application
• Step 2: Using app, gathered 25 sets of benchmark images • cover a range of common photography settings • 4,303 jpeg images (23 × 167 + 2 × 231, one for each
focus position)• Canon EOS 550D/Rebel T2i camera
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Experimental methodology: Comparative evaluation of focus measures for digital photography
• Step 3: Determined ground truth• true lens position (or image) where an object is in best
focus
• Step 4: Implemented more than 30 focus measures• extensive survey of the literature
• Step 5: Given a benchmark set of images and a focus measure• applied focus measure to each jpeg image in benchmark • focus measure predicts where an object will be in best
focus• given predictions of focus measure and ground truth,
calculated precision, recall, and mean absolute error
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Experimental methodology: Comparative evaluation of focus measures for digital photography
ground truthtrue false
predicted
truetp
(true positive)
fp(false
positive)
falsefn
(false negative)
tn(true
negative)
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Experimental methodology: Precision and recall
=tp
precisiontp fp
=tp
recalltp fn
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squared gradient Laplacian
3=
3 0precision
3=
3 1recall
4=
4 0precision
4=
4 0recall
• MAE chosen over mean squared error • MAE prefers errors that are occasionally large but small on
average• mean square error prefers errors that avoid large errors
while still possibly being quite unsatisfactory overall
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Experimental methodology: Mean absolute error (MAE)
p p absolute error =
where p is lens position of image in maximal focus
is lens position that focus measure predictsp
Focus measure precision
recall MAE
Brenner 100.00 99.00 0.00squared gradient 100.00 99.00 0.003 × 3 difference 98.00 97.00 0.023 × 3 Sobel 98.00 97.00 0.023 × 3 Scharr 98.00 97.00 0.023 × 3 Roberts 98.00 97.00 0.023 × 3 Prewitt 98.00 97.00 0.02Gaussian 95.00 92.00 0.05vertical sq. gradient
91.33 92.00 0.55
vertical Brenner 91.33 90.00 0.23
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Experimental results: First-order differentiation
Focus measure precision
recall MAE
Laplacian of Gaussian
98.00 99.00 0.32
5 × 5 vertical Sobel
96.67 99.00 0.65
5 × 5 Laplacian 96.67 99.00 0.465 × 5 cross Sobel 90.33 93.00 0.663 × 3 cross Sobel 89.67 93.00 1.183 × 3 vertical Sobel
88.73 96.00 3.94
3 × 3 Laplacian 85.00 91.00 1.415 × 5 horizontal Sobel
83.33 88.00 1.08
3 × 3 horizontal Sobel
73.27 78.00 2.95February 4, 2014 Focus Measures for Digital Photography 21
Experimental results : Second-order differentiation
Focus measure precision
recall MAE
normalized variance
43.57 53.00 26.36
variance 32.33 35.00 20.80threshold pixel count
4.24 18.00 52.38
threshold content 2.13 4.00 36.31power 0.53 2.00 43.80
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Experimental results: Image statistics
Focus measure precision
recall MAE
autocorrelation 80.40 99.00 26.87Vollath's F4 61.74 87.00 24.60
Vollath's F5 33.00 35.00 19.00
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Experimental results: Correlation
• Results:• some popular focus measures perform poorly when applied
to autofocusing in digital photography or to more representative sets of images• simple focus measures based on taking the first derivative
of an image perform exceedingly well in digital photography, although care must be taken in which direction derivative is taken
April 8th 2013Combinatorial Problems in Compiler
Optimization24
Experimental results: Discussion
• The speed and accuracy of a digital camera's contrast-based autofocus algorithm are crucial to user satisfaction
• We advocate using three standard statistical measures of performance—precision, recall, and mean absolute error—as accuracy criteria
• Our experimental results indicate that two simple focus measures based on taking first derivative of an image perform exceedingly well in digital photography
February 4, 2014 Focus Measures for Digital Photography 25
Conclusion