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Document image sharpening using a new extension of the aperture filter

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Abstract

A new extension to the aperture filter is proposed to sharpen document images. The aperture filter is a nonlinear filter applied within a window having both domain and range constraints. The proposed aperture filter incorporates an adaptation to the original design by utilizing gradient directions of the input document images. Results demonstrate that the performance of the new approach is superior to that of both the aperture filter and alternative sharpening methods.

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Abbreviations

\({\bf{\Psi}}\) :

signal filter

A :

aperture filter

D(i, j) :

edge vector, where D(i, j) = (d x i, j , d y i, j )

dz :

four-dimensional feature vector, where d z  =  (d x1, dx2, dy1, dy2)

E[Y|X]:

conditional probability of Y given X

E i :

Euclidean distance

I :

ideal signal

I*:

clipped ideal signal

[ − k, k]:

amplitude range of the aperture filter

K x , K y :

two convolution kernels (5  ×  5 masks) of Sobel operators

q :

number of clusters

T :

predefined threshold in the proposed aperture filter

[ − w, w]:

window domain of the aperture filter

X :

observed signal, X  =  (x 0, x 1, x 2, . . .)

X*:

clipped observed signal, \({X^{\ast}{=}({x}_{0}^{\ast}, x_{1}^{\ast}, x_{2}^{\ast}, {\ldots}}\)

x(i, j):

an image pixel

Y :

estimation of the true signal

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Authors and Affiliations

  1. Department of Electronic and Electrical Engineering, University of Strathclyde, 204 George Street, Glasgow, G1 1XW, UK

    Tarek A. Mahmoud & Stephen Marshall

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  1. Tarek A. Mahmoud
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  2. Stephen Marshall
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Correspondence to Tarek A. Mahmoud.

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Mahmoud, T.A., Marshall, S. Document image sharpening using a new extension of the aperture filter. SIViP 3, 403–419 (2009). https://doi.org/10.1007/s11760-008-0090-3

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