Gaussian smoothing and its first and second differentials are very important for image processing and computer vision. We already have methods based on the sliding Fourier transform (SFT) in order to calculate Gaussian smoothing efficiently. However, errors in floating point calculation accumulate quickly when we use the single-precision floating-point format. Also, the resultant discontinuities at the edges of SFT intervals generate false extreme points easily. To resolve the abovementioned problems, we propose the attenuated SFT (ASFT) by introducing a decay factor to the original SFT together with a new criterion for determining coefficients to effectively approximate Gaussian function and its differentials. Extensive experiments demonstrate a decisive superiority of the proposed ASFT over the original SFT.

GAT (Global Affine Transformation) and GPT (Global Projection Transformation) correlation matchings were successively proposed by Wakahara and Yamashita which use affine transformation (AT) and 2D projection transformation (PT), respectively, to maximize the normalized cross-correlation value between a template and a GAT/GPT-superimposed input image. In theory, to maximize the degree of matching via normalized cross-correlation, the L2 norm of both images should be normalized. However, the criteria of conventional GAT/GPT correlation techniques did not take account of the conservation of the L2 norm. This research solves the above-mentioned problem which might impair the matching ability of GAT/GPT correlations. In particular, we focus on the enhanced GPT correlation recently proposed by Wakahara et al. to calculate optimal PT parameters simultaneously. Then, we propose an improved criterion satisfying the requirement of the L2 norm conservation together with the enhanced GPT correlation algorithm with norm normalization. Experimental results using artificially deformed images of chess board and handwritten digits from MNIST database by 2D projection transformation show that the proposed method clearly outperforms those conventional GPT correlation techniques with or without norm normalization in terms of both convergence speed and matching ability.

This paper describes a new technique of 2D projection transformation invariant template matching, GPT (Global Projection Transformation) correlation, as a natural extension of our earlier work on the affine-invariant GAT (Global Affine Transformation) correlation method. The key ideas are threefold. First, we show that arbitrary 2D projection transformation (PT) can be decomposed into a product of affine transformation (AT) and partial projection transformation (PPT). Second, we propose an efficient computational model for determining sub-optimal components of AT and PPT separately that maximize a normalized cross-correlation value between an either AT- or PPT-superimposed input image and a template by solving linearized simultaneous equations. Third, we obtain optimal components of combined AT and PPT, i.e. PT, that maximize a normalized cross-correlation value between a PT-superimposed input image and a template via the successive iteration method. The proposed technique has the time complexity of O(n2), where n equals the number of pixels. Experiments using templates and their artificially distorted images as input images show that the proposed method is far superior to the GAT correlation method in 2D projection transformation tolerance, and, also, has a high tolerance for noise.

The global affine transformation (GAT) correlation method proposed by Wakahara et al. is a pattern matching method that can compensate for affine transformation embedded in an input pattern. The GAT correlation method demonstrated a high performance in character recognition and object matching. For example, it outperformed the well-known tangent distance (TD) method in character recognition experiments made on IPTP handwritten numeral database. The purpose of this paper is threefold. First, we introduce a new matching measure called the nearest neighbor distance of equi-gradient direction (NNDEGD) in cooperation with the GAT correlation method. The NNDEGD is just the window parameter of the Gaussian function used in the GAT correlation method, which is equal to the average minimum distance between a point in one image and another point in the other image with the same gradient direction. We propose to use this value as a new matching measure. Secondly, we extend the GAT correlation method so as to handle the change of stroke width besides the affine transformation. Finally, we apply the original and extended versions of the GAT correlation method to fc-NN classification experiments using the MNIST database. These experiments are carried out efficiently for the first time because we have substantially reduced the computational complexity and memory load involved in the original GAT correlation method. We successfully show that the enhanced GAT correlation method has achieved the lowest error rate of 0.49% compared with competing distortion-tolerant template matching techniques.

Fisher discriminant analysis (FDA) is a very famous analysis method for classification. However, FDA does give an optimal projection only for Gaussian distributions with equal covariance matrices. In other words, FDA is not optimal in the case of heteroscedastic Gaussian distributions. In this paper, we propose a novel criterion for FDA including a correction term based on the Bhattacharyya distance which is closely related to classification rate. Furthermore, the Chernoff distance based criterion and its kernelized version are proposed as its extension. These proposed criteria have three strong points. The first one is that the correction term based on the Bhattacharyya distance can deal with heteroscedastic Gaussian distributions. The second one is that the correction term based on the Chernoff distance can handle easily the difference in the number of class samples. The third point is that their kernel extensions are easily implemented to be applied to non-Gaussian distributions. As a result, the proposed method is applicable in a wide variety of classification problems. Experimental results using toy simulations and nine kinds of UCI real-world datasets show marked advantages of the proposed method over the conventional FDA.

This paper addresses the problem of reinforcing the ability of k-NN classification of handwritten characters via distortion-tolerant template matching techniques with a limited quantity of data. We make a comparison of three kinds of matching techniques: the conventional simple correlation, the tangent distance, and the GAT (Global Affine Transformation) correlation. The k-NN classification method is straightforward and powerful, however, is very time-consuming. Hence, to reduce the computational cost of matching in k-NN classification we propose to accelerate the GAT correlation technique by reformulating its computational model and adopting efficient lookup tables. Recognition experiments made on the handwritten numerical database IPTP CDROM1B show that matching techniques of the simple correlation, the tangent distance, and the accelerated GAT correlation achieve recognition rates of 97.07%, 97.50%, and 98.70%, respectively. Also, the computation time ratios of the tangent distance and the accelerated GAT correlation to the simple correlation are 26.3 and 36.5 to 1.0, respectively.

This paper addresses the problem of binalizing multicolored character strings in scene images subject to heavy image degradations and complex backgrounds. The proposed method consists of four steps. The first step generates tentatively binarized images via every dichotomization of K clusters obtained by K-means clustering of constituent pixels of a given image in the HSI color space. The total number of tentatively binarized images equals 2^K-2. The second step divides each binarized image into a sequence of "single-character-like" images using an average aspect ratio of a character. The third step is use of support vector machines (SVM) to determine whether each "single-character-like" image represents a character or non-character. We feed the SVM with the mesh feature to output the degree of "character-likeness." The fourth step selects a single binarized image with the maximum average of "character-likeness" as an optimal binarization result. Experiments using a total of 1000 character strings extracted from the ICDAR 2003 robust word recognition dataset show that the proposed method achieves a correct binarization rate of 80.8%.

This paper proposes a new, affine-invariant image matching technique via accelerated KL (Kullback-Leibler) divergence minimization. First, we represent an image as a probability distribution by setting the sum of pixel values at one. Second, we introduce affine parameters into either of the two images' probability distributions using the Gaussian kernel density estimation. Finally, we determine optimal affine parameters that minimize KL divergence via an iterative method. In particular, without using such conventional nonlinear optimization techniques as the Levenberg-Marquardt method we devise an accelerated iterative method adapted to the KL divergence minimization problem through effective linear approximation. Recognition experiments using the handwritten numeral database IPTP CDROM1B show that the proposed method achieves a much higher recognition rate of 91.5% at suppressed computational cost than that of 83.7% obtained by a simple image matching method based on a normal KL divergence.

This paper proposes a new technique for binalizing multicolored characters subject to heavy degradations. The key ideas are threefold. The first is generation of tentatively binarized images via every dichotomization of k clusters obtained by k-means clustering in the HSI color space. The total number of tentatively binarized images equals 2k-2. The second is use of support vector machines (SVM) to determine whether and to what degree each tentatively binarized image represents a character or non-character. We feed the SVM with mesh and weighted direction code histogram features to output the degree of “character-likeness.” The third is selection of a single binarized image with the maximum degree of “character likeness” as an optimal binarization result. Experiments using a total of 1000 single-character color images extracted from the ICDAR 2003 robust OCR dataset show that the proposed method achieves a correct binarization rate of 93.7%.

This paper addresses the problem of how to extract, describe, and evaluate handwriting deformation from the deterministic viewpoint for improving recognition accuracy. The key ideas are threefold. The first is to extract handwriting deformation vector field (DVF) between a pair of input and target images by 2D warping. The second is to hierarchically decompose the DVF by a parametric deformation model of global/local affine transformation, where local affine transformation is iteratively applied to the DVF by decreasing window sizes. The third is to accept only low-order deformation components as natural, within-class handwriting deformation. Experiments using the handwritten numeral database IPTP CDROM1B show that correlation-based matching absorbing components of global affine transformation and local affine transformation up to the 3rd order achieved a higher recognition rate of 92.1% than that of 87.0% obtained by original 2D warping.

This paper addresses the problem of improving the accuracy of character recognition with a limited quantity of data. The key ideas are twofold. One is distortion-tolerant template matching via hierarchical global/partial affine transformation (GAT/PAT) correlation to absorb both linear and nonlinear distortions in a parametric manner. The other is use of multiple templates per category obtained by k-means clustering in a gradient feature space for dealing with topological distortion. Recognition experiments using the handwritten numerical database IPTP CDROM1B show that the proposed method achieves a much higher recognition rate of 97.9% than that of 85.8% obtained by the conventional, simple correlation matching with a single template per category. Furthermore, comparative experiments show that the k-NN classification using the tangent distance and the GAT correlation technique achieves recognition rates of 97.5% and 98.7%, respectively.

The discriminant function of a subspace method is provided by using correlation matrices that reflect the averaged feature of a category. As a result, it will not work well on unknown input patterns that are far from the average. To address this problem, we propose two kinds of weighted correlation matrices for subspace methods. The globally weighted correlation matrix (GWCM) attaches importance to training patterns that are far from the average. Then, it can reflect the distribution of patterns around the category boundary more precisely. The computational cost of a subspace method using GWCMs is almost the same as that using ordinary correlation matrices. The locally weighted correlation matrix (LWCM) attaches importance to training patterns that are near to an input pattern to be classified. Then, it can reflect the distribution of training patterns around the input pattern in more detail. The computational cost of a subspace method with LWCM at the recognition stage does not depend on the number of training patterns, while those of the conventional adaptive local and the nonlinear subspace methods do. We show the advantages of the proposed methods by experiments made on the MNIST database of handwritten digits.

This paper addresses the basic problem of how to extract, describe, and evaluate handwriting deformation from not the statistical but the deterministic viewpoint. The key ideas are threefold. The first idea is to apply 2D warping to extraction of handwriting deformation vector field (DVF) between a pair of input and target images. The second idea is to hierarchically decompose the DVF by a parametric deformation model of global/local affine transformation. As a result, the DVF is expressed by a series of deformation components each of which is characterized by a window size of local affine transformation. The third idea is interrupting of the series of deformation components to obtain natural, reasonable handwriting deformation. Experiments using the handwritten numeral database IPTP CDROM1B show that 31.1% of the handwriting DVF is expressed by global affine transformation, and the subsequent few local affine transformations successfully discriminate natural handwriting deformation from unnatural one.

This paper proposes a new technique of figure-ground discrimination of color characters in scene images following two steps. The first step is temporary binarization by selecting one optimal projection axis in the RGB color space and a threshold value along the axis using Otsupsilas criterion as a two-class classification problem. The second step is figure-ground determination based on the figure-to-ground ratio on the image periphery and common characteristics that a character pattern should have. Next, regarding distortion-tolerant character recognition under the condition of a small sample size we compare our global affine transformation (GAT) correlation method against the well-known tangent distance, where both methods use only a single template for each of 62 alphanumeric characters. Experiments are made on a total of 698 character images extracted from the ICDAR 2003 robust OCR dataset. The proposed figure-ground discrimination method achieves a correct binarization rate of 75.3%. Next, in recognition of correctly binarized characters the GAT correlation method and the tangent distance realize correct recognition rates of 94.1% and 91.6%, respectively. Moreover, the GAT correlation method is found to outperform the tangent distance in robustness against rotation at an angle of more than 20 degrees.

Optimal binarization of degraded grayscale characters is a crucial step to subsequent character recognition. This paper proposes a new, promising binarization technique of grayscale characters using genetic algorithms (GA) to search for an optimal sequence of filters from among a set of rather simple, representative image processing filters. First, we classify degraded samples of grayscale characters into several categories. Then, in the learning stage, by selecting a training sample from each degradation category we apply GA to the combinatorial optimization problem of determining a sequence of filters that maximizes the fitness value between the filtered training sample and its target image ideally binarized by humans. Finally, in the testing stage, we apply the optimal sequence of filters thus obtained to remaining test samples for each degradation category. Experiments using the public ICDAR 2003 robust OCR dataset demonstrate promising results of binarization of grayscale characters against a wide variety of degradation causes.

This paper addresses the problem of how to construct a robust character classifier when statistical pattern recognition techniques fail because of a limited quantity of data. The key ideas are two ways. One is to adopt a distortion-tolerant shape matching technique. Here, we use an affine-invariant matching technique of global affine transformation (GAT) correlation to absorb linear distortion between grayscale images. The other is to prepare multiple templates for dealing with nonlinear distortion or topologically different shapes. For this purpose, K-means clustering is applied to a given limited data in a simple gradient feature space. Recognition experiments using the handwritten numeral database IPTP CDROMIB show that the proposed method achieves a much higher recognition rate of 97.2% as compared to that of 85.8% obtained by the conventional, simple correlation matching with a single template per category.

This paper proposes a new technique of segmentation and recognition of characters with a wide variety of image degradations and complex backgrounds in natural scenes. The key ideas are twofold. One is segmentation of character and background by local/adaptive binarization of one of Cyan/Magenta/Yellow (CMY) color planes with the maximum breadth of histogram. The other is affine-invariant grayscale character recognition using global affine transformation (GAT) correlation. In experiments, we use a total of 698 test images extracted from the public ICDAR 2003 robust OCR dataset containing images of single characters in natural scenes. In advance, we classify those images into seven groups according to the degree of image degradations and/or background complexity. On the other hand, we prepare a single-font set of 62 alphanumerics for templates. Experimental results show an average recognition rate of 70.3%, ranging from 95.5% for clear images to 24.3% for little-contrast images.

This paper addresses the problem of to what extent linear transformation can alleviate nonlinear distortion. We investigate a technique of global affine transformation (GAT) correlation to absorb linear distortion between gray-scale images. Features used in GAT correlation are occurrence probabilities of black pixels or gradients. Experiments using the handwritten numeral database IPTP CDROM1B show that the entropy of GAT-superimposed images decreases by around 15%. Furthermore, gray-level-based GAT correlation improves the recognition rate from 85.78% to 91.01%, while gradient-based GAT correlation improves the recognition rate from 91.80% to 94.02%. These results show that GAT correlation has a marked effect of improving both shape matching and discrimination abilities by extracting linear distortion from nonlinear one.

This paper proposes a new, promising character recognition system with a category-dependent normalization technique that normalizes an input pattern against each reference pattern adaptively using global affine transformation (GAT) as follows. (1) An input character pattern is fed to "the basic OCR, " the most powerful of the conventional OCRs. (2) The basic OCR plays the role of rough classification and outputs a small set of candidate categories for the input pattern. (3) GAT normalizes the input pattern against each candidate reference pattern adaptively. (4) Each adaptively normalized input pattern is fed again to the basic OCR. (5) The final recognition result is obtained using the updated "distance " values within candidate categories. In experiments, our basic OCR linked to GAT adaptive normalization is successfully applied to 28,694 patterns of totally unconstrained handwritten characters, including Kanji, Kana, and alphanumerics, written by 300 people, with substantial improvements in recognition accuracy.

Describes a technique of gray-scale character recognition that offers both noise tolerance and affine-invariance. The key ideas are twofold. First is the use of normalized cross-correlation as a matching measure to realize noise tolerance. Second is the application of global affine transformation (GAT) to the input image so as to achieve affine-invariant correlation with the target image. In particular, optimal GAT is efficiently determined by the successive iteration method using topographic features of gray-scale images as matching constraints. We demonstrate the high matching ability of the proposed GAT correlation method using gray-scale images of numerals subjected to random Gaussian noise and a wide range of affine transformation. Moreover, extensive recognition experiments show that the achieved recognition rate of 94.3 percent against rotation within 30 degrees, scale change within 30 percent, and translation within 20 percent of the character width along with random Gaussian noise is sufficiently high compared to the 42.8 percent offered by simple correlation.

This paper describes a new technique of gray-scale character recognition that offers both noise-tolerance and affine-invariance. The key ideas are twofold. First is the use of normalized cross-correlation to realize noise-tolerance. Second is the application of global affine transformation (GAT) to the input image so as to achieve affine-invariant correlation with the target image. In particular, optimal GAT is efficiently determined by the successive iteration method. We demonstrate the high matching ability of the proposed method using gray-scale images of numerals subjected to random Gaussian noise and a wide range of affine transformation. The achieved recognition rate of 92.1% against rotation within 30 degrees, scale change within 30%, and translation within 20% of the character width is sufficiently high compared to the 42.0% offered by simple correlation.

Introduces a new technique of affine-invariant correlation of gray-scale characters by reinforcing correlation-based matching in two ways. The first method is the use of normalized cross-correlation as a matching measure based on definite canonicalization in order to realize robustness against image degradation. The second method is the application of an iterative global affine transformation (GAT) to the input image, so as to realize the maximal affine-invariant correlation with the target image. The advantages and effectiveness of the proposed method are both shown theoretically and demonstrated through preliminary experiments using gray-scale images of numerals subject to a wide range of affine transformations and random Gaussian noise.

The mean shift method, a simple iterative clustering procedure that shifts each data point to the average of data points in its neighborhood, is being extended in three ways: 1) the window parameter controlling the size of the neighborhood is automatically determined from the original distribution of points; 2) stable, hierarchical clustering is achieved by increasing the window parameter value in a deterministic manner; and 3) the guarantee of its convergence is rigorously proven. A critical comparison of the extended mean shift method to the k-means method and other hierarchical clustering methods is made using artificial 2D point distributions of overlapping Gaussians and half-circles with random noise. Moreover, the extended mean shift method has successfully been applied to the clustering of a wide variety of handwriting deformation in a 256-dimensional feature space.

This paper introduces an adaptive or category-dependent normalization method that normalizes an input pattern against each reference pattern using global/local affine transformation (GAT/LAT) in a hierarchical manner as a general deformation model. Also, the normalization criterion is clearly defined as minimization of the mean of nearest-neighbor interpoint distances between each reference pattern and a normalized input pattern. Optimal GAT/LAT is determined by iterative application of weighted least-squares fitting techniques. Experiments using input patterns of 3,171 character categories, including Kanji, Kana, and alphanumerics, written by 36 people in the cursive style against square-style reference patterns show that the proposed method not only can absorb a fairly large amount of handwriting fluctuation within the same category, but the discrimination ability is greatly improved by the suppression of excessive normalization against similarly shaped but different categories. Furthermore, comparative results obtained by the conventional shape normalization method for preprocessing are presented.

Conventional normalization methods for handwritten characters have limitations, such as preprocessing operations because they are category-independent. The paper introduces an adaptive or category-dependent normalization method that normalizes an input pattern against each reference pattern using global/local affine transformation (GAT/LAT) in a hierarchical manner as a general deformation model. Experiments using input patterns of 3171 character categories, including Kanji, Kana, and alphanumerics, written by 36 people in the cursive style against square style reference patterns show not only that the proposed method can absorb a fair large amount of handwriting fluctuation within the same category, but also that discrimination ability is greatly improved by the suppression of excessive normalization against similarly shaped but different categories.

We present a distortion-tolerant online cursive Kanji character recognition method that absorbs the stroke-based handwriting distortion expressible by uniform affine transformation. Experiments are made using two kinds of test data in the square style and in the cursive style for 2,980 Kanji character categories; recognition rates of 98.4 percent and 96.0 percent are obtained.

This paper describes a distortion-tolerant online Kanji character recognition method using stroke-based affine transformation (SAT). The first part of the method determines one-to-one stroke correspondence between an input pattern and each reference pattern. The second part applies optimal SAT to each stroke of the input pattern to absorb handwriting distortion. The last part calculates the inter-pattern distance between the reference pattern and the SAT-superimposed input pattern. Only a single reference pattern for each of 2,980 Kanji character categories is generated by using training data written carefully with the correct stroke-number and stroke-order. Recognition tests are made using two kinds of test data in the square style and in the cursive style written by 36 different people; recognition rates of 98.4% and 96.0% are obtained.

This paper describes a stroke-number and stroke-order free on-line Kanji character recognition method by a joint use of two complementary algorithms of optimal stroke correspondence determination: one dissolves excessive mapping and the other dissolves deficient mapping. Also, three kinds of inter-stroke distances are devised to deal with stroke concatenation or splitting and heavy shape distortion. Only a single reference pattern for each of 2,980 Kanji character categories is generated by using training data composed of 120 patterns written with the correct stroke-number and stroke-order. Recognition tests are made using the training data and two kinds of resting data in the square style and in the cursive style written by 36 different people; recognition rates of 99.5%, 97.6%, and 94.1% are obtained.

This paper describes an iterative technique for gradually deforming a mask binary image with successive local affine transformation (LAT) operations so as to yield the best match to an input binary image as one new and promising approach toward robust handwritten character recognition. The method uses local shapes in the sense that the LAT of each point at one location is optimized using locations of other points by means of least-squares data fitting using Gaussian window functions. It also uses a multiscale refinement technique that decreases the spread of window functions with each iteration. Especially in handwritten character recognition, structural information is indispensable for robust shape matching or discrimination. The method is enhanced to explicitly incorporate structures by weighting the above least-squares criterion with similarity measures of both topological and geometric features of the mask and input images. Moreover, deformation constraints are imposed on each iteration, not only to promote and stabilize matching convergence but also to suppress an excessive matching process. Shape matching experiments have been successfully carried out using skeletons of totally unconstrained handwritten numerals.>

For large-alphabet languages, like Japanese, handwriting input using an online recognition technique is essential for input accuracy and speed. However, there are serious problems that prevent high recognition accuracy of unconstrained handwriting. First, the thousands of ideographic Japanese characters of Chinese origin (called Kanji) can be written with wide variations in the number and order of strokes and significant shape distortions. Also, writing box-free recognition of characters is required to create a better man-machine interface. Intense research performed over the past 15 years to answer the most pressing recognition problems is described. Prototype systems are also described. The man-machine interfaces made possible by online handwriting recognition and anticipated advances in both hardware and software are discussed.>

The author describes an iterative technique for gradually deforming a mask dot image with successive local affine transformation (LAT) operations so as to yield the best match to an nput dot image. The method uses local structure in the sense that the LAT of a dot at one location is optimized using locations of other dots by means of least-squares data fitting with Gaussian window functions. A multiscale or coarse-fine strategy has been implemented in the algorithm by decreasing the effective interacting neighborhood with each iteration. This technique successfully extracted distortions or displacements from dot images of handwritten figures and random-dot stereograms.>

This survey describes the state of the art of online handwriting recognition during a period of renewed activity in the field. It is based on an extensive review of the literature, including journal articles, conference proceedings, and patents. Online versus offline recognition, digitizer technology, and handwriting properties and recognition problems are discussed. Shape recognition algorithms, preprocessing and postprocessing techniques, experimental systems, and commercial products are examined.>

The state of the art of online handwriting recognition is surveyed based on an extensive review of the literature. Shape recognition algorithms, preprocessing and postprocessing techniques, experimental systems, and commercial products are examined. It is found that online recognizers, except for bar-code readers and other specialized equipment, are not applicable to machine-printed characters.>