The document describes a new superpixel segmentation algorithm called Superpixels Using Morphology (SUM) and compares it to existing algorithms. SUM uses a watershed transformation approach on an image's morphological gradient that has undergone area closing to efficiently generate superpixels. In experiments on rock images, SUM achieved under-segmentation error and boundary recall comparable to recent algorithms while being significantly faster, making it suitable for applications requiring fast superpixel generation.

1. Superpixels Using Morphology for Rock Image
Segmentation
Sree Ramya s. P. Malladi, Sundaresh Ram and Jeffrey J. Rodriguez
Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ, USA
Email: {rmalladi.ram.jjrodrig}@email.arizona.edu
Abstract-Detection and segmentation of rocks is an important
first task in many applications such as geological analysis,
planetary science and mining processes. Rocks are usually
segmented using a variety of features such as texture, shading,
shape and edges. It is easier to compute these features for rock
superpixels rather than every pixel in the image. A superpixel
is a group of spatially coherent pixels that form a meaningful
homogeneous region, usually belonging to the same object. In this
paper, we perform a comparative study of some of the current
superpixel algorithms on rock images with regard to their ability
to adhere to image boundaries, their speed, and their impact
on rock segmentation performance. Also, we propose a new and
very simple superpixel algorithm, Superpixels Using Morphology
(SUM), which permutes a watershed transformation approach to
efficiently generate superpixels. We show that SUM achieves a
performance comparable to the recent superpixel algorithms on
the rock images.
Index Terms-morphology, watershed segmentation, area clos­
ing, superpixels, rock particles.
I. INTRODUCTION
Detection and segmentation of rock particles IS Important
in order to measure the size distribution of rock particles
in mining processes to monitor the blasting quality, optimize
the blast design, and reduce costs and environmental impact.
Also, rock shape, weathering, and dispersion carry important
information about environmental characteristics and need to
be identified for efficient route planning in planetary science.
Superpixel segmentation is an attempt to capture the low-level
details in image by grouping the pixels such that they pro­
vide spatial support for extracting features. Superpixels show
benefit in applications such as object tracking [1], detection
[2], segmentation [3], depth estimation [4] and object-based
compression.
Rock image segmentation can be thought of as a two­
step process. First, superpixels are computed, and then a
region merging scheme is used to merge the superpixels into
a final segmentation. In this paper, we focus on computing
superpixels. The superpixels computed for the rock images
are expected to have the following properties:
1) Superpixel boundaries should accurately represent, the
edges of the rocks.
2) A superpixel should not include portions of more than
one rock. (Because post-processing is expected to in­
clude a merging step, it is easier to recover from
oversegmentation than undersegmentation.)
3) The technique for computing superpixels should be
computationally simple and memory efficient.
978-1-4799-4053-0114/$31.00 ©2014 IEEE 145
Many algorithms have been recently developed to divide an
image into superpixels [5]-[8], [10]-[15]. We compare four
algorithms: normalized cuts (Ncuts) [5], turbopixels [12],
simple iterative linear clustering (SLIC) [13], entropy rate
superpixels (ERS) [14] and the proposed method, superpixels
using morphology (SUM). Ncuts treats the image as a graph
G = (V, E), where the vertices V represent the pixel locations
and the edges E represent the relation between the pixels (ver­
tices). This graph is partitioned using contour and texture cues,
globally minimizing a cost function defined on the edges at
the partition boundaries. Run time for Ncuts is relatively large.
Turbopixels uses a level-set based geometric flow to dilate a set
of initially placed seeds defined by the user. This algorithm re­
lies on other algorithms of varying complexity and sometimes
exhibits relatively poor adherence to the boundaries. SLIC is
a variation of k-means clustering for generating superpixels.
SLIC optimizes the distance calculations by limiting the search
space, and uses a weight parameter to control the compactness
of superpixels. For SLIC the segmentation accuracy critically
depends on how well this weight parameter is tuned. ERS
is a graph topology selection method where pixels and their
pairwise relations are respectively mapped to the vertices and
edges in the graph. Superpixels are then formed via graph
topology by maximizing an objective function. The objective
function has two components: (1) the entropy rate which
favors compact and homogeneous superpixels and (2) the
balancing term which favors superpixels with similar sizes.
ERS produces a segmentation with reasonable accuracy, but
the run-time may be too long for many applications.
In this paper, we describe a new superpixel segmentation
method using a modified watershed segmentation algorithm.
The algorithm is composed of three key steps: (1) compute
the magnitude gradient of the original image, (2) perform an
area closing operation on this magnitude gradient image, and
(3) apply a watershed transformation to the resultant image to
obtain the desired superpixels.
II. SUPERPIXELS USING MORPHOLOGY
We describe a new method for computing the superpixels in
an image, using morphology-based operators, which is faster
than the existing algorithms and is very memory efficient. The
new method, superpixels using morphology, is adapted from
the watershed segmentation algorithm [9].
SSIAI2014

2. Fig. I. (a) Original image. (b) Morphological gradient image (inverted) with a 3 x 3 square. (c) Closing of gradient magnitude image (inverted) with a disk
(r = 10). (d) Area closing of gradient magnitude image (inverted) (0: = 100). (e) Watershed lines obtained from image (c) superimposed onto original image.
(f) Watershed lines obtained from image (d) superimposed onto original image.
A. Image Gradient
Object boundaries are often characterized by intensity tran­
sitions (edges) in the image. Various gradient operators are
widely used in image processing to detect these edges, the
basic principle being that large gradients indicate points where
there is a rapid intensity change. We compute the morpholog­
ical gradient of the input image f defined by
gradb(f) = (f EB b) - (f e b), (1)
where b is a structuring element, usually symmetric and having
a short support, EB is a morphological dilation operation, and
e is a morphological erosion operation. We use a 3 x 3
square-shaped structuring element b for computing the mor­
phological gradient image. Fig. lea) shows an example image,
and Fig. l(b) shows the corresponding morphological gradient
magnitude image.
B. Morphological Area Closing
The morphological gradient image may consist of spurious
strong local gradients within a single rock region due to gray­
level variations, in addition to having true strong gradients near
the rock edges. A classical approach to suppress such spurious
gradients in the gradient image is the use of the morphological
closing operator. When there is no prior infonnation about
the shape of an object in an image, morphological closing
is usually perfonned with a disk-shaped structuring element
to preserve isotropy. Fig. l(c) shows the effect of applying
morphological closing to the gradient image in Fig. l(b). The
closing operation is then followed by watershed segmentation
to obtain the segmented image. However, artifacts may appear
in the segmented image. Fig. lee) shows an example of such
artifacts, where the crest lines have moved many pixels away
from the actual boundary of the object. The extent of the
deviation depends on the filtering strength (i.e., the radius of
the disk).
In order to suppress the spurious gradients in the morpho­
logical gradient image, along with the associated segmentation
artifacts, we employ Vincent's morphological area closing
operator [17]. The gray-scale formulation of this operator
relies on the threshold superposition principle and is given
by
(2)
where,
BBe,a = {X c E: X is Be-connected, Area(X) 2 o:}
This operator removes connected components whose area
is smaller than a given area parameter 0:. This morphological
filter is shape preserving because it acts on connected compo­
nents and, therefore, does not typically change the shape of
the structures in the image. We use a fast implementation of
this operator by Meijster and Wilkinson [18]. Fig. led) shows
the result of applying the area closing operator to the gradient
image in Fig. l(b).
C. Watershed Segmentation
The watershed transformation [9] is a popular segmentation
algorithm, which divides the gray-level image into regions
that are each associated with one local minimum. Consider
the gray-level image as a topographic map. For each regional
minimum of this map, define a catchment basin (i.e., a
region) as all those points whose steepest-slope paths reach
this minimum. The watershed lines are then defined as the
closed one-pixel-thick crest lines that separate the adjacent
catchment basins. Due to numerous local minima present
within an image, applying watershed segmentation directly
to the image ends up in extreme over-segmentation. We
apply the watershed segmentation algorithm to the area-closed
gradient image to obtain the desired superpixels. Fig. 1(0
shows the watershed lines obtained by applying the watershed
segmentation algorithm to the area-closed gradient image in
Fig. led), superimposed onto the original image.
III. PERFORMANCE EVALUATION
To analyze the quality of superpixel segmentation, two met­
rics are used: under-segmentation error and boundary recall.
Manually segmented "ground truth" images are used as a
reference to compute the metrics.
A. Under-Segmentation Error (U)
Under-segmentation error [16] measures false merging of
superpixels across the ground truth borders. A superpixel
is considered to be falsely merged if it spans across a
ground truth border. Consider a ground truth segmentation
comprising M segments {gl' g2' . . . , 9M} and a corresponding
automatic superpixel segmentation comprising L segments
{8l' 82,• • •
, 8L}' Let N be the number of pixels in the image,
146

3. .. . . . . . . . . . . . . . . . . . . . . .
-TP
-sue
-ERS
" 'SUM
-Nellts
500 1()()() 1500 2()()() 2500
Number ofSegments
Fig. 2. (a). Under-segmentation error (b). Boundary recall.
and let the operator 1·1 represent the size of a segment in pixels.
The under-segmentation error is a value within the range [0,1],
with 0 meaning no under-segmentation error, and is defined
as
M
u = �L L min{lsjl-lsjngil,lsjngil}-M
i=l {SjICISjngil)",¢}
(3)
B. Boundary Recall (�)
Boundary recall measures the fraction of ground truth
boundaries that fall within a fixed distance from a superpixel
boundary. Consider a ground truth segmentation GT and a
superpixel segmentation S. Let TP represent the number of
boundary pixels in GT that have a boundary pixel in S within a
distance of 2 pixels. Let FN represent the number of boundary
pixels in GT for which there does not exist a boundary pixel
in S within a distance of 2 pixels. Boundary recall is a value
in the range [0,1]' and is defined as
TP
� =
TP+FN
(4)
C. Experiments
The recent superpixel algorithms [5], [12], [13], [14] and the
proposed method SUM were tested on a set of 10 rock images.
Each image has size 480 x 640 pixels. A careful manual
segmentation of the rock images was considered as ground
truth for all subsequent analysis. On average, each rock image
has around 50 to 100 ground truth rock regions. The dataset of
rock images includes rocks with varying illumination, shading,
shape, and texture. The goal of the superpixel algorithms
should be to produce a minimum number of superpixels with
good segmentation quality (low under-segmentation error and
high boundary recall). The run time of the algorithms is also
an important factor.
We used open source implementations of the superpixel
algorithms available online. The original implementation of
the Ncuts algorithm resizes the image to 160 x 160 for faster
compution. We disable the image resizing poperty of Ncuts
algorithm and keep the size of the image fixed for all the
methods to have a fair comparison. The number of superpixels
is the only parameter used by the turbopixel algorithm. SLIC
has two parameters: region size (to produce uniformly sized
TABLE 1
RUN TIME IN SECONDS FOR DIFFERENT ALGORITHMS
# of
Turbo ERS SLIC Ncuts SUM
Segments
25 14.310 2.045 0.650 158.349 0.020
500 39. 110 2.910 1.699 1802.600 0.024
1000 41.201 3.641 1.731 0.027
2500 44.036 5.741 1.960 0.044
regions) and regularizer (to control the compactness). The
region size was fixed, and the regularizer that gave the least
under-segmentation error was chosen. The region sizes were
chosen so as to give the same number of segments as the
other methods for fair comparison. ERS has four parameters:
number of superpixels, weighting factor for the balancing
function, Gaussian kernel parameter, and connectedness (4-
connected or 8-connected). The number of superpixels was
fixed, and the combination of other parameters that gave
the least under-segmentation error was chosen. For the rock
images tested, the optimal range of superpixels lies between
250 and 500. Thus, we compared the performance of all the
algorithms in this operating range.
The under-segmentation error measures the amount of false
merging, so we want to minimize this error. Fig. 2(a) shows
a plot of the under-segmentation error vs. the number of
superpixels for all the automated methods. In the range of 250-
500 superpixels, the difference between the SUM algorithm
and the other methods is very small. The under-segmentation
error of Ncuts and ERS is 0.03 less than SUM. The under­
segmentation error of SLIC and the turbopixel algorithm is
just 0.007 less than SUM.
Boundary recall measures the adherence of superpixel
boundaries to ground truth image boundaries, so we want to
maximize this quantity. Fig. 2(b) shows that the boundary re­
call of SUM is comparable to the other superpixel algorithms.
The boundary recall of SUM is 0.2 greater than turbopixels.
The boundary recall of ERS, SLIC, and Ncuts is 0.07 greater
than SUM.
All the automated algorithms were run on a 2.5 GHz Intel
core is processor with 4 GB RAM. Table I compares the run
time of all the algorithms. SUM outperforms all the algorithms
under study with respect to run time. In the operating range,
SUM is 1.674 seconds faster than SLIC and 2.886 seconds
faster than ERS. The algorithms are ranked in the following
order with respect to run time: SUM, SLIC, ERS, Turbopixels,
and Ncuts.
Fig. 3 shows the superpixel segmentation results for an
example rock image. Typically, the superpixel segmentation
would next undergo post-processing in order to merge the
oversegmented regions.
IV. CONCLUSION
In this paper, we compared recent superpixel segmentation
algorithms on rock images. The Ncuts algorithm gives compa­
rable results to the rest of the automated algorithms in tenns
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4. (d) (e) (f)
Fig. 3. (a) Original image. Results of the automated algorithms: (b) Ncuts, (c) turbopixels, (d) SLIC, (e) ERS, (f) SUM (proposed method).
of under-segmentation and boundary recall, but requires more
computation time. ERS and SUC perform well in terms of
under-segmentation and boundary recall and are also faster
than turbopixels and Ncuts. SUM is the fastest among all the
algorithms and simple to implement when compared to the
other methods. At the same time, its under-segmentation and
boundary recall are comparable to ERS and SUe. Next, we
plan to implement various region merging schemes to combine
with these superpixe algorithms in order to determine which
algorithm gives the most accurate final segmentation.
ACKNOWLEDGMENT
We would like to thank Split Engineering LLC for providing
the rock image data set.
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