Pattern Recognition 40 (2007) 456 – 475 www.elsevier.com/locate/patcog Convex hull based skew estimation Bo Yuan a , ∗ , Chew Lim Tan b a Centre for Remote Imaging, Sensing and Processing, National University of Singapore, Singapore b Department of Computer Science, School of Computing, National University of Singapore, Singapore Received 16 August 2005; received in revised form 27 January 2006; accepted 1 February 2006 Abstract Skew estimation and page segmentation are the two closely related processing stages for document image analysis. Skew estimation needs proper page segmentation, especially for document images with multiple skews that are common in scanned images from thick bound publications in 2-up style or postal envelopes with various printed labels. Even if only a single skew is concerned for a document image, the presence of minority regions of different skews or undefined skew such as noise may severely affect the estimation for the dominant skew. Page segmentation, on the other hand, may need to know the exact skew angle of a page in order to work properly. This paper presents a skew estimation method with built-in skew-independent segmentation functionality that is capable of handling document images with multiple regions of different skews. It is based on the convex hulls of the individual components (i.e. the smallest convex polygon that fully contains a component) and that of the component groups (i.e. the smallest convex polygon that fully contain all the components in a group) in a document image. The proposed method first extracts the convex hulls of the components, segments an image into groups of components according to both the spatial distances and size similarities among the convex hulls of the components. This process not only extracts the hints of the alignments of the text groups, but also separate noise or graphical components from that of the textual ones. To verify the proposed algorithms, the full sets of the real and the synthetic samples of the University ofWashington English Document Image Database I (UW-I) are used. Quantitative and qualitative comparisons with some existing methods are also provided.  2006 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved. Keywords: Document processing; Skew estimation; Component grouping; Page segmentation; Convex hulls; Segregation effect; UW-I 1. Introduction Printed documents are customarily rectangular. Ideally, text lines in documents are horizontal or vertical relative to the edges of the pages. Due to the imprecision or difficulty in the placement of the original documents in the scanning process, the captured edges of the documents may not al- ways align with the edges of the images. This amount of misalignment is usually referred to as the skew angle of an image. Skew estimation is one of the important processing steps in document image understanding. There are some in- depth reviews [1–4] and comparative evaluations [5] avail- able for the large array of techniques that have been devel- oped in the research literature [6–26]. ∗ Corresponding author. Tel.: +6565165389. E-mail address: yuanbo@nus.edu.sg (B. Yuan). 0031-3203/$30.00  2006 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.patcog.2006.02.016 There are various hints of skew in a textual document image. The most explored reference of orientation is the straight text lines. To approximate these text lines, various strategies are deployed, among which the most popular are the projection-profile based [6–11], the Hough-transform based [12–16], the nearest-neighborhood based [17–19], the morphological operation based [20–22], and the spatial fre- quency based [23–26]. Different skew estimation methods compete on the ground of detection accuracy, time and space efficiencies, abilities to detect the existence of multi- ple skews in the same image, and robustness in noisy envi- ronments and scan-introduced distortions. A typical projection-profile based skew estimation method uses a single point, called fiducial point, to represent each component in an image. The set of fiducial points are pro- jected onto a 1-D accumulator array along an angle and a chosen premium function is evaluated on the accumulator