Measuring the degree to which a shape resembles a polygon (referred to as polygonality) is a difficult problem due to the intrinsic diversity in the form and distortion of shapes caused by digitization and similarity transformation. This paper proposes a generic approach for this problem by performing the measurement in the projection space where the Radon image of some primitive shapes, which compose the shape, becomes apparent. The obtained measures take value in (0, 1] with 1 corresponding to analytical polygons. They are robust to additive noise and boundary distortion, and is invariant to similarity transformation. The new framework generalizes existing polygonal measures such as triangularity and quadrangularity. In addition, the ability to estimate polygon's geometric quantities in the projection space allows approximating a shape by analytical polygons. The efficiency of the proposed approach is demonstrated through a number of experiments on both synthetic and real data sets.

Generic polar harmonic transforms have recently been proposed to extract rotation-invariant features from images and their usefulness has been demonstrated in a number of pattern recognition problems. However, direct computation of these transforms from their definition is inefficient and is usually slower than some efficient computation strategies that have been proposed for other methods. This paper presents a number of novel computation strategies to compute these transforms rapidly. The proposed methods are based on the inherent recurrence relations among complex exponential and trigonometric functions used in the definition of the radial and angular kernels of these transforms. The employment of these relations leads to recursive and addition chain-based strategies for fast computation of harmonic function-based kernels. Experimental results show that the proposed method is about 10× faster than direct computation and 5× faster than fast computation of Zernike moments using the q-recursive strategy. Thus, among all existing rotation-invariant feature extraction methods, polar harmonic transforms are the fastest.

A new parametric method for edge noise removal in graphical document images is presented using geometrical regularities of the graphics contours that exists in the images. Denoising is understood as a recovery problem and is done by employing a sparse representation framework with a basis pursuit denoising algorithm for denoising and curvelet frames for encoding directional information of the graphics contours. The optimal precision parameter used in this framework is shown to have linear relationship with the level of the noise. Experimental results show the superiority of the proposed method over existing ones in terms of image recovery and contour raggedness.

A class of rotation-invariant orthogonal moments is proposed using a complex exponential in the radial direction. Each member of this class, while sharing beneficial properties to image representation and recognition like orthogonality and rotation-invariance, has distinctive properties depending on the value of a parameter, making it more suitable for some particular applications. The computation of moments is simpler and more stable than existing methods. Experimental results show the effectiveness of this class of moments in term of description performance and pattern recognition ability.

A novel text extraction method from graphical document images is presented in this paper. Graphical document images containing text and graphics components are considered as two-dimensional signals by which text and graphics have different morphological characteristics. The proposed algorithm relies upon a sparse representation framework with two appropriately chosen discriminative overcomplete dictionaries, each one gives sparse representation over one type of signal and non-sparse representation over the other. Separation of text and graphics components is obtained by promoting sparse representation of input images in these two dictionaries. Some heuristic rules are used for grouping text components into text strings in post-processing steps. The proposed method overcomes the problem of touching between text and graphics. Preliminary experiments show some promising results on different types of document.

A new shape descriptor invariant to geometric transformation based on the Radon, Fourier, and Mellin transforms is proposed. The Radon transform converts the geometric transformation applied on a shape image into transformation in the columns and rows of the Radon image. Invariances to translation, rotation, and scaling are obtained by applying 1D Fourier-Mellin and Fourier transforms on the columns and rows of the shape's Radon image respectively. Experimental results on different datasets show the usefulness of the proposed shape descriptor.

Automatic processing of images of steles is a challenging problem due to the variation in their structures and body text characteristics. In this paper, area Voronoi diagram is used to represent the neighborhood of connected components in stele images containing Nom characters. Body text region is then extracted from stele images by the selection of appropriate adjacent Voronoi regions based on the information about the thickness of neighboring connected components. Experimental results show that the proposed method is highly accurate and robust to various types of stele.