Elsevier

Pattern Recognition

Volume 39, Issue 1, January 2006, Pages 89-101
Pattern Recognition

Efficient computation of adaptive threshold surfaces for image binarization

https://doi.org/10.1016/j.patcog.2005.08.011Get rights and content

Abstract

The problem of binarization of gray level images, acquired under non-uniform illumination is reconsidered. Yanowitz and Bruckstein proposed to use for image binarization an adaptive threshold surface, determined by interpolation of the image gray levels at points where the image gradient is high. The rationale is that high image gradient indicates probable object edges, and there the image values are between the object and the background gray levels. The threshold surface was determined by successive over-relaxation as the solution of the Laplace equation. This work proposes a different method to determine an adaptive threshold surface. In this new method, inspired by multiresolution approximation, the threshold surface is constructed with considerably lower computational complexity and is smooth, yielding faster image binarizations and often better noise robustness.

Introduction

Let us consider the problem of separating objects from their background in a gray level image I(x,y), where objects appear lighter (or darker) than the background. This can be done by constructing a threshold surface T(x,y), and constructing a binarized image B(x,y) by comparing the value of the image I(x,y) with T(x,y) at every pixel, viaB(x,y)=1ifI(x,y)>T(x,y),0ifI(x,y)T(x,y).It is clear that a fixed value of the threshold surface T(x,y)=const cannot yield satisfactory binarization results for images obtained under non-uniform illumination and/or with a non-uniform background.

Chow and Kaneko in Ref. [1] were among the first researchers to suggest using adaptive threshold surfaces for binarization. In their method the image was divided into overlapping cells, and sub-histograms of gray levels in each cell were calculated. Sub-histograms judged to be bimodal were used to determine local threshold values for the corresponding cell centers, and the local thresholds were interpolated over the entire image to yield a threshold surface T(x,y). This was certainly an improvement over fixed thresholding, since this method utilized some local information. However, the local information was implicitly blurred to the size of the cell, and this, obviously, could not be decreased too much.

Yanowitz and Bruckstein made a step forward in Ref. [2] by suggesting to construct a threshold surface by interpolating the image gray levels at points where the image gradient is high. Indeed, high image gradients indicate probable object edges, where the image gray levels are between the object and the background levels. The threshold surface was required to interpolate the image gray levels at all support points and to satisfy the Laplace equation at non-edge pixels. The surface was determined by a successive over-relaxation method (SOR) [2], [3].

Trier and Taxt conducted a performance evaluation of 15 binarization methods by comparing the performance of OCR system with respective binarization method as the first step [4]. The Yanowitz–Bruckstein (YB) method produced the best results with the Trier–Taxt method just slightly behind. After the addition of a ghost-elimination step from Yanowitz and Bruckstein method, the methods of Niblack [5], Eikvil–Taxt–Moen [6] and Bernsen [7] performed slightly better.

As will be shown later, the last three methods are not scale-invariant, and their performance is optimal only for some specific object sizes or requires parameter tuning. The Yanowitz–Bruckstein method is scale invariant, however the computational complexity of successive over-relaxation method is expensive: O(N3) for an N×N image and the resulting binarization process is slow, especially for large images. Furthermore, the threshold surface tends to have sharp extremum at the support points, and this can degrade the binarization performance.

We here follow the approach of Yanowitz and Bruckstein and use image values at the support high gradient points to construct a threshold surface. However, we define a new threshold surface via a method inspired by multiresolution representation [8]. The new threshold surface is constructed as a sum of functions, formed by scaling and shifting of a given original function. This new threshold surface can be stored in two ways: as an array of coefficients aljk, or as a conventional threshold surface T(x,y) which is obtained as a sum of scaled and shifted source functions, multiplied by appropriate coefficients aljk.

The threshold surface coefficients aljk are determined in O(Plog(N)) time, where P is the number of support points and N2 is the image size. These coefficients can then be used to construct the threshold surface T(x,y) over the entire image area N2 in O(N2log(N)) time or to construct the threshold surface over smaller region of the image of M2 size in only O(M2log(N)) time. Furthermore, the adaptive threshold surface can be made smooth over all the image domain.

The rest of this paper is organized as follows: Section 2 reviews the best performing methods according to Trier and Taxt evaluation [4], Niblack [5], Eikvil–Taxt–Moen [6], Bernstein [7], and Yanowitz–Bruckstein [2]. Section 3 describes a proposed new method to construct a threshold surface. Section 4 describes the implementation of the surface computation. Section 5 presents some experimental results, comparing the speed and binarization performance of the proposed method with the methods of Niblack and Yanowitz–Bruckstein. Finally Section 6 summarizes this work with some concluding remarks.

Section snippets

Niblack's method

The idea of this method is to set the threshold at each pixel, based on the local mean and local standard deviation. The threshold at pixel (x,y) is calculated asT(x,y)=m(x,y)+k·s(x,y),where m(x,y) and s(x,y) are the sample mean and standard deviation values, respectively, in a local neighborhood of (x,y). The size of the neighborhood should be small enough to reflect the local illumination level and large enough to include both objects and the background. Trier and Taxt recommend to take 15×15

The new threshold surface

We propose to construct and represent the threshold surface as a sum of functions, obtained by scaling and shifting of a single source function, similar to what is done in wavelets or multiresolution representations [13]. In multiresolution representation [8] the coefficients are calculated on the basis of an original signal that is known a priori. In our case the complete threshold surface is not known in advance, but only its approximate values at the support points: T(pi)=I(pi)vi. Here pi={x

Implementation

The algorithm described in the previous section was implemented in Matlab. The subsections below describe the data structures and then the algorithm implementation.

Experimental results

The three methods, YB with adaptive threshold surface obtained by SOR and the new one with adaptive threshold surface obtained by multiresolution approximation and the Niblack's method were compared for speed and quality of binarization. The programs were implemented in MATLAB and ran on an IBM-Thinkpad-570 platform with 128 MB RAM and a Pentium-II 366 MHz processor.

Four artificial black–white images were generated by simulating non-uniform illumination of the black and white pattern. This

Concluding remarks

In this work we proposed a new way to construct a threshold surface in order to improve the Yanowitz–Bruckstein binarization method. The new threshold surface is constructed with considerably lower computational complexity and hence in much shorter time even for small images. The new method allows even more gain in speed in region-of-interest processing scenarios. The new threshold surface can be made smooth and by the nature of its construction should be similar to the local illumination

About the Author—ILYA BLAYVAS received his B.Sc. from the faculty of aerophysics and space research of Moscow Institute of Physics and Technology (MIPT) in 1992, and his M.Sc. (with honours) in laser physics from Ben Gurion University in 1996. In 1996–1999 he designed Monolitic Microwave Integrated Circuits at Israely Armament Development Authority, and in 2000–2001 he performed an electro-optical characterization of CMOS image sensors at Tower Semiconductor ltd. From 2001 he is doing his Ph.D.

References (13)

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About the Author—ILYA BLAYVAS received his B.Sc. from the faculty of aerophysics and space research of Moscow Institute of Physics and Technology (MIPT) in 1992, and his M.Sc. (with honours) in laser physics from Ben Gurion University in 1996. In 1996–1999 he designed Monolitic Microwave Integrated Circuits at Israely Armament Development Authority, and in 2000–2001 he performed an electro-optical characterization of CMOS image sensors at Tower Semiconductor ltd. From 2001 he is doing his Ph.D. research in Computer Vision at CS Department of Technion.

About the Author—ALFRED M. BRUCKSTEIN received the B.Sc. (honors) and M.Sc. in electrical engineering from the Technion, Israel Institute of Technology, Haifa, and his Ph.D. in electrical engineering from Stanford University, Stanford, CA, in 1977, 1980, and 1984, respectively. Since 1985, he has been a Faculty Member at the Technion, Israel Institute of Technology, where he currently a full Professor, holding the Ollendorff Chair in Science. During the summers from 1986 to 1995 and from 1998 to 2000 he was a Visiting Scientist at Bell Laboratories, and in 2001-2002 a visiting chaired professor at Tsing-Hua Univarsity in Beijing, China. He served on the editorial boards of Pattern Recognition, Imaging Systems and Technology, Circuits Systems, and Signal Processing. He also served as a member of program committees of 20 conferences. His research interests are in Image and Signal processing, Computer Vision, Computer Graphics, Pattern Recognition, Robotics (especially Ant Robotics), Applied Geometry, estimation theory and inverse scattering, and neuronal encoding process modeling. Prof. Bruckstein is a member of SIAM, AMS, and MM and is presently the dean of the Technion Graduate school. He was awarded the Rothschild Fellowship for Ph.D. Studies at Stanford, Taub Award, Theeman Grant for a scientific tour of Australian Universities, and the Hershel Rich Technion Innovation Award twice.

About the Author—RON KIMMEL received his B.Sc. (with honors) in computer engineering in 1986, the M.S. degree in 1993 in electrical engineering, and the D.Sc. degree in 1995 from the Technion–Israel Institute of Technology. During the years 1986–1991 he served as an R&D officer in the Israeli Air Force.

During the years 1995–1998 he has been a postdoctoral fellow at the Computer Science Division of Berkeley Labs, and the Mathematics Department, University of California, Berkeley. Since 1998, he has been a faculty member of the Computer Science Department at the Technion, Israel, where he is currently an associate professor. He is now a visiting Professor at the Computer Science Department, Stanford University, and working with MediGuide Inc.

His research interests are in computational methods and their applications in: Differential geometry, numerical analysis, image processing and analysis, and computer graphics. He was awarded the Hershel Rich Technion innovation award (twice), the Henry Taub Prize for excellence in research, Alon Fellowship, the HTI Postdoctoral Fellowship, and the Wolf, Gutwirth, Ollendorff, and Jury fellowships.

He has been a consultant of HP research Lab in image processing and analysis during the years 1998–2000, and to Net2Wireless/Jigami research group during 2000–2001. He is on the advisory board of MediGuide (biomedical imaging 2002–2005), and has been on various program and organizing committees of conferences, workshops, and editorial boards of image processing and analysis journals, like International Journal of Computer Vision, and IEEE Trans. on Image Processing.

He is the author of ‘Numerical Geometry of Images’ published by Springer, November 2003.

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