morphological filters. Then a ‘‘flat zone’’ area filter is presented,
leading to the definition of the morphological neighborhood.
2.1. Introduction
Mathematical morphology provides high-level non-linear
operators to analyze spatial inter-pixel dependency in an image
[25]. Morphological operators have already proven their potential
in remote-sensing image processing [7]. Two widely used mor-
phological operators are opening and closing by reconstructions
[26]. They are connected operators that satisfy the following
assertion: If the structure of the image cannot contain the
structuring element (SE), then it is totally removed, else it is
totally preserved. For a given SE, geodesic opening or geodesic
closing provides a characterization of the size or shape of some
objects present in the image: The objects that are smaller than the
SE are deleted while others (that are bigger than the SE) are
preserved. To determine the shape or size of all elements present
in an image, it is necessary to use a range of different SE sizes.
This concept is called Granulometry [23,12,27]. When granulome-
try is built with connected operators, such as opening by
reconstruction [26], the image is progressively simplified while
no shape-noise is introduced. In that case, the resulting image
contains only maxima which have a larger size than the structur-
ing element of size
l
: The structuring element can fit in each
maximum. If area openings are used, the output image has its
maxima that contain more than
l
pixels (the area is seen as the
number of pixels inside a maximum).
This concept has given rise to the morphological profile (MP)
for the analysis of remote-sensing images: The concatenation of a
granulometry and anti-granulometry made with geodesic filters
[28]. Fig. 1 gives an example of an MP obtained with three
openings (closings) by reconstruction with a disk, respectively,
of radius 5, 13 and 21 as structuring element.
Geodesic opening and closing filters are interesting because
they preserve shapes. However, they cannot provide a complete
analysis of urban areas because they only act on the extrema of
the image. Moreover, some structures may be darker than their
neighbors in some parts of the image, yet lighter than their
neighbors in others. Although this problem can be partially
addressed by using an alternate sequential filter (ASF) [29], the
MP thus provides an incomplete description of the inter-pixel
dependency.
In [22], Soille has proposed using self-complementary filters
(the definition is given in the next section) to analyze all the
structures of an image, local extrema, be they minima or maxima,
as well as regions with intermediate gray-levels. This assumes
that any given structure of interest corresponds to one set of
connected pixels. Based on an area criterion, a self-complemen-
tary flat zone filter is proposed to remove small structures [22].
This kind of filter is well suited to the analysis of high resolution
optical images: The very high spatial resolution results in exces-
sively detailed data containing many irrelevant structures (e.g.
cars on the road). As will be detailed in the following, the area
self-complementary filter is not a morphological filter, since the
increasingness property no longer holds. Thus, the granulometry
strategy used with the MP cannot be directly applied. In this
work, another approach is proposed to extract the contextual
information. The idea is to build an adaptive neighbors system for
each pixel [30], which considers neighboring pixels that belong to
the same structure. In the following, the self-complementary flat
zone area filter is presented as an alternative to the original
granulometry operator, and the neighborhood definition is
detailed.
2.2. Area filtering
As explained in the previous section, classic opening/closing-
based filters (granulometry or ASF) have the same limitation,
i.e. they act on the maxima/minima of the image. Hence, the
simplification of the image only occurs for structures that are
extrema, whereas many structures corresponding to homoge-
neous intermediate regions are not processed. The consequence is
an incomplete filtering of the structures of interest. Example of
such a problem is shown in Fig. 2. Fortunately, flat zone
approaches can tackle this problem [31].
A flat zone is a connected (in 8-connectivity) region where the
gray-level is constant [32]. Flat zone filtering consists in removing
all the flat zones that do not fulfill a given criterion. In this paper,
the objective is to remove all the structures that are ‘‘too small’’ to
be significant in a morphological meaning, e.g. the road is usually
a class of interest but not the cars that might be on the road.
Fig. 1. Morphological profile: The left part of the profile corresponds to the anti-granulometry and the right part to the granulometry.
Fig. 2. (a) Original image, (b) ASF based on area opening/closing, (c) flat zones area
filtering and (d) the neighborhood system. For both filters
l
was set to 10. Note
that with ASF, many structures are of an area smaller than
l
. Using
c
area
l
, the
number of flat zones significantly decreases, from 1995 flat zones in (a) to 127 in
(c), against 1242 in (b). In (d) each color represents a set of neighbor pixels.
M. Fauvel et al. / Pattern Recognition 45 (2012) 381–392 383