Adaptive thresholding in binarization

CVL – Daeyong @ GIST, Korea

Date : 2014. 11. 18Presenter : Dae-Yong Cho

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Contents

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What is binarization?

Binarization Method• Otsu’s• Sauvola’s

References

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What is binarization?

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Divide image’s intensities into 0 or 255 (Foreground and Background )

Color Image

Gray Image

Binary Image

Thresholding

𝑇

𝟎 , 𝑖𝑓 𝐼<𝑇𝐼𝑏𝑖𝑛𝑎𝑟𝑦=¿𝟏 , h𝑜𝑡 𝑒𝑟𝑤𝑖𝑠𝑒

Used for OCR System to segment characters from background

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Binarization Method

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Otsu

Sauvola

Niblack

Bernsen

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Binarization Method - Otsu

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h𝐴𝑙𝑔𝑜𝑟𝑖𝑡 𝑚

1. Compute histogram of input image

2. Compute probabilities of each intensity level (0 to 255)

3. Step through all possible thresholds

4. Select threshold corresponds to the

(Assumption : There are only two classes in histogram)

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Binarization Method - Otsu

CVL – Daeyong @ GIST, Korea

h𝐴𝑙𝑔𝑜𝑟𝑖𝑡 𝑚

1. Compute histogram of input image

2. Compute probabilities of each intensity level (0 to 255)

3. Step through all possible thresholds

4. Select threshold corresponds to the

(Assumption : There are only two classes in histogram)

Histogram

Gray Scale Image

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Binarization Method - Otsu

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1. Compute histogram of input image

2. Compute probabilities of each intensity level (0 to 255)

3. Step through all possible thresholds

4. Select threshold corresponds to the

(Assumption : There are only two classes in histogram)

𝐶𝑙𝑎𝑠𝑠 1 𝐶𝑙𝑎𝑠𝑠 2

𝝎𝟏 𝝎𝟐

𝑡𝑖

•

•

•

h𝐴𝑙𝑔𝑜𝑟𝑖𝑡 𝑚

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Binarization Method - Otsu

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1. Compute histogram of input image

2. Compute probabilities of each intensity level (0 to 255)

3. Step through all possible thresholds

4. Select threshold corresponds to the

(Assumption : There are only two classes in histogram)

𝑡𝑖𝐶𝑙𝑎𝑠𝑠 1 𝐶𝑙𝑎𝑠𝑠 2

𝝎𝟏 𝝎𝟐

𝜎𝜔2 (𝑡 )=𝜔1 (𝑡 )𝜎1

2 (𝑡 )+𝜔2 (𝑡 )𝜎22 (𝑡 )

𝜎 𝑏2 (0 )=𝛼 ,𝜎 𝑏

2 (1 )=𝛽 ,𝜎𝑏2 (2 )=𝛾 , …

h𝐴𝑙𝑔𝑜𝑟𝑖𝑡 𝑚

𝜇1 𝜇2𝑚

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Binarization Method - Otsu

CVL – Daeyong @ GIST, Korea

1. Compute histogram of input image

2. Compute probabilities of each intensity level (0 to 255)

3. Step through all possible thresholds

4. Select threshold corresponds to the

(Assumption : There are only two classes in histogram)

𝑡𝑖𝐶𝑙𝑎𝑠𝑠 1 𝐶𝑙𝑎𝑠𝑠 2

𝝎𝟏 𝝎𝟐

𝜎 𝑏2 (0 )=𝛼

𝜎 𝑏2 (1 )=𝛽

𝜎 𝑏2 (2 )=𝛾

𝜎 𝑏2 (255 )=𝛿

Select which makes largest

h𝐴𝑙𝑔𝑜𝑟𝑖𝑡 𝑚

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Binarization Method - Otsu

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Result

Input Image Otsu Alg. Output

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Binarization Method - Otsu

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Result

Input Image Otsu Alg. Output

Effect of Global Method

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Binarization Method - Sauvola

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Local Method Do not use histogram anymore

Compute threshold for each pixel

I

𝑻 𝟏 𝑻 𝒏

𝑻 𝒌 𝑻 𝒑

To overcome Otsu’ algorithm’s problem

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Binarization Method - Sauvola

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Local Threshold Value t(x,y)

𝑡 (𝑥 , 𝑦 )=𝑚 (𝑥 , 𝑦 ) [1+𝑘( 𝑠 (𝑥 , 𝑦 )𝑅

−1)]

(𝑥 , 𝑦 )

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Binarization Method - Sauvola

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Local Threshold Value

𝑡 (𝑥 , 𝑦 )=𝑚 (𝑥 , 𝑦 ) [1+𝑘( 𝑠 (𝑥 , 𝑦 )𝑅

−1)] ,𝑘=[0.2,0 .5]

𝐹𝑜𝑟 𝑤𝑖𝑛𝑑𝑜𝑤𝑠𝑖𝑧𝑒=3 (𝑥 , 𝑦 )

•

𝑤𝑥

𝑤𝑦

•

𝑂 (𝑤2𝑀𝑁 )

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Binarization Method - Sauvola

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Input Image Sauvola Alg. Output (with k = 0.5)

Result

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Binarization Method - Sauvola

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Input Image

Sauvola Alg. Output (Elapsed time : 484msec)

Comparison

Otsu Alg. Output (Elapsed time : 16msec)

Computation Cost Results of Reference [2]

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References

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1. WikiPedia : http://en.wikipedia.org/wiki/Otsu's_method

2. T. Romen Singh, Sudipta Roy, O. Imocha Singh, Tejmani Sinam, and Kh. Manglem Singh, “A

New Local Adaptive Thresholding Technique in Binarization”, International Journal of Com-

puter Science Issuses(IJCSI), Vol. 8, Issue 6, No 2, November 2011.

3. Faisal Shafait, Daniel Keysers, and Thomas M. Breuel, “Effiecient Implementation of Local

Adaptive Thresholding Techniques Using Integral Images”, International Society for Optics and

Photonics(SPIE), 2008.

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Q & A

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