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transform, has highlighted the need for architectures th
large one-dimensional windows, to which the optimisations in the aforementioned architectures do not apply.
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www.ietdl.orgA set of architectures for computing both the median and weighted median of large, flexibly sized windows
through parallel cumulative histogram construction is presented. The architecture uses embedded memories
to control the highly parallel bank of histogram nodes, and can implicitly determine window sizes for median
and weighted median calculations. The architecture is shown to perform at 72 Msamples, and has been
integrated within a Trace transform architecture.
1 Introduction
The median filter is a highly versatile non-linear filter that has
been used extensively in a variety of domains. Its strength lies
in its ability to filter out noise while minimally affecting the
properties of the underlying signal. The median filter replaces
a sample with the middle ranked value among all the samples
within the sample window, centred around the sample in
question. In this manner, it filters out samples that are not
representative of their surroundings; in other words, outliers.
In the image processing domain, a two-dimensional median
filter allows for the removal of ‘salt-and-pepper’-type noise
from an image without adversely affecting the underlying
edges. The use of a linear filter (such as a Gaussian or mean
filter) in this situation would cause a blurring of edges. The
median filter can still degrade image quality somewhat,
although the preservation of edges is paramount in the
computer vision domain. Such filters within image processing
are almost uniquely two-dimensional and have small window
sizes.
Our recent work with the Trace transform [1, 2] highlighted
the need for a hardware architecture to compute median and
weighted median values on large one-dimensional windows.
The Trace transform is a recently introduced algorithm that
has been shown to perform well in a variety of image
recognition and categorisation tasks, including image database
search, face authentication and distortion correction [3]. It
maps a standard image to an alternative domain and, while
defining the spatial mapping, is general in terms of
mathematical computation. The transform involves the
computation of mathematical functions on lines crossing an
image. Two of the functions typically used are the median
and weighted median. Given that these lines can traverse the
whole image, the number of sample points is of similar
magnitude to the dimensions of the image, typically hundreds
of pixels. Furthermore, given that the length of these lines is
not fixed, a hardware architecture must cope with variable
window sizes. The weighted median presents its own
challenge in implementation terms, and we believe the work
presented here and originally introduced in [4] to be the first
hardware implementation of weighted median filters on large
windows.
The median of a set of samples is often computed by
sorting the input samples and then selecting the middle
value. The weighted median can be computed in multiple
stages: first expanding the weighted sample sequence, thenPublished in IET Computers & Digital Techniques
Received on 18th September 2008
Revised on 22nd January 2009
doi: 10.1049/iet-cdt.2008.0119
High-throughput one-d
and weighted median fi
S.A. Fahmy1 P.Y.K. Cheung2 W
1CTVR, Trinity College Dublin, Dublin 2, Ireland
2Department of Electrical and Electronic Engineering, Imperia
3Department of Computing, Imperial College London, London
E-mail: suhaib.fahmy@tcd.ie
Abstract: Most effort in designing median filters has foc
used for image processing. However, recent work onThe Institution of Engineering and Technology 2009ISSN 1751-8601
ensional median
lters on FPGA
. Luk3
College London, London SW7 2AZ, UK
W7 2AZ, UK
ed on two-dimensional filters with small window sizes,
ovel image processing algorithms, such as the Trace
at can compute the median and weighted median ofIET Comput. Digit. Tech., 2009, Vol. 3, Iss. 4, pp. 384–394
doi: 10.1049/iet-cdt.2008.0119