IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 8, NO. 1, JANUARY 1999 69
Image Segmentation and Analysis via
Multiscale Gradient Watershed Hierarchies
John M. Gauch, Member, IEEE
Abstract—Multiscale image analysis has been used successfully
in a number of applications to classify image features according
to their relative scales. As a consequence, much has been learned
about the scale-space behavior of intensity extrema, edges, inten-
sity ridges, and grey-level blobs. In this paper, we investigate
the multiscale behavior of gradient watershed regions. These
regions are defined in terms of the gradient properties of the
gradient magnitude of the original image. Boundaries of gradient
watershed regions correspond to the edges of objects in an image.
Multiscale analysis of intensity minima in the gradient magnitude
image provides a mechanism for imposing a scale-based hierarchy
on the watersheds associated with these minima. This hierarchy
can be used to label watershed boundaries according to their
scale. This provides valuable insight into the multiscale properties
of edges in an image without following these curves through
scale-space. In addition, the gradient watershed region hierarchy
can be used for automatic or interactive image segmentation. By
selecting subtrees of the region hierarchy, visually sensible objects
in an image can be easily constructed.
Index Terms—Image segmentation, multiscale image analysis,
watershed regions.
I. INTRODUCTION
M
ULTISCALE image analysis and image segmentation
play an important role in many computer vision appli-
cations. Together, they provide an indication of where visually
sensible objects in an image are located and also information
about their relative size or importance. With this information,
it is possible to perform quantitative measurements of object
properties such as size, shape, position, and orientation, and to
accomplish higher level vision tasks such as object recognition.
Early multiresolution methods utilized somewhat ad hoc res-
olution reduction schemes, but they produced compact image
descriptions which were useful for a number of computer
vision tasks [7], [38]. Gaussian blurring was later introduced to
study the scale-space behavior of intensity extrema in signals
and images [26], [44]. One of the attractive properties of this
technique is that images simplify in a well behaved manner.
For example, Gaussian blurring does not create any zero
crossings as resolution is reduced [1], [45].
The multiscale behavior of a number of image features have
been examined. Paths traced by intensity extrema through
Manuscript received March 31, 1995; revised November 1, 1996. This work
was supported in part by a grant from the Whitaker Foundation, the National
Science Foundation (CDA-9401 021), and the National Cancer Institute (CA-
42 165).The associate editor coordinating the review of this manuscript and
approving it for publication was Prof. William E. Higgins.
The author is with the Department of Electrical Engineering and Com-
puter Science, University of Kansas, Lawrence, KS 66045 USA (e-mail:
jgauch@eecs.ukans.edu).
Publisher Item Identifier S 1057-7149(99)00220-1.
scale-space have been used to study one-dimensional (1-D)
signals [11], [44]. The image stack is the result of similar
analysis of critical points in two-dimensional (2-D) images
[26]. This multiscale image representation has also been used
for image segmentation [27]. The multiscale behavior of grey-
level blobs (defined relative to intensity extrema) has been
used to develop a scale-space primal sketch and used for
image segmentation and analysis [28]. The performance of
both of these segmentation techniques suffered somewhat
because edge information was not explicitly included. Edges
defined by Laplacian of Gaussian zero crossings [30] and zeros
of directional derivatives [8], [20] have been traced through
multiple scales in an attempt to identify significant object
boundaries and deal with image noise [2], [22]. One problem
with these methods is the difficulty of retaining connected
edge segments through scale-space. A second difficulty is
constructing object regions from these boundaries.
The multiscale behavior of intensity ridges and valleys
in an image have also been studied [15]. Ridge tops and
valley bottoms were defined in terms of the local differential
geometry of the image (extrema of level curve curvature) and
followed through scale-space. This process results in well
localized ridges and valleys but involves costly multiscale
curve following. To simplify this analysis, a representation for
ridge tops and valley bottoms based on watershed boundaries
was utilized. The drainage patterns of simulated rainfall on an
image can be used to partition an image into watershed regions
called hills and dales [9], [31]. The boundaries of hills corre-
spond to ridge tops and the boundaries of dales correspond to
valley bottoms, so multiscale watershed analysis provides an
alternative method to study the scale-space behavior of ridges
and valleys in an image [16].
Mathematical morphology provides a powerful set of non-
linear image analysis tools which can be applied in a wide
variety of situations [13], [21], [41]. For example, images
can be segmented into visually sensible regions by finding
the watershed regions in a gradient magnitude image [32],
[42]. Oversegmentation is a well-known difficulty with this
approach, which has led to a number of approaches for merg-
ing watershed regions to obtain larger regions corresponding to
objects of interest [17], [19], [34], [39], [40]. The development
of morphological scale-space operations [10], [23] has also
made it possible to study the multiscale behavior of watershed
regions [24], [25]. One advantage of this approach is that no
new intensity extrema (or corresponding watershed regions)
are created as scale is increased. In spite of recent speed
improvements [5], [14] the mathematical morphology scale-
space approach remains computationally demanding.
1057–7149/99$10.00
1999 IEEE
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