possibility for mass production. Rotifer is also valuable for larval fish because of its amino acid composition and high digestibility Watanabe et al., 1983, it can be
enriched with fatty acids and antibiotics, and can be used to transfer these substances into fish larvae Lubzens et al., 1989.
Estimating the density of rotifers is a general method for assessing and monitor- ing the physiological condition of rotifer cultures Hoff and Snell, 1997. This
assessment depends upon the computation of the number of rotifers and carried eggs. Since rotifers are small, a sample from the culture tank needs to be examined
under a microscope, so that the number of rotifers as well as carried eggs can be counted one by one. Although this is important, the counting is time-consuming
and labor-intensive Fulks and Main, 1991. Further, errors might be introduced due to worker’s fatigue and carelessness. Hence, the development of an automatic
system to substitute for human counters is required.
Rotifers are similar in shape, except when bearing eggs. Rotifer size has been reported in the range of 123 – 292 mm in length and 114 – 199 mm in width Snell and
Carrillo, 1984. The body size of rotifers is primarily genetically determined which changes with environmental factors like temperature, salinity, or food type. Rotifers
have a repeatedly parthenogenetic life cycle that contains both asexual and sexual phases. The eggs produced from the sexual phase are slightly bigger in size and are
more spherical than those from the asexual phase with smooth oval appearance. Sexual eggs are covered with tough shells. The shells protect the eggs from extreme
environments Hoff and Snell, 1997.
The major objective of this study was to develop a system for the rotifer identification using pattern recognition under a microscope. Following the conven-
tional operation steps, a shape analysis technique is to be employed to characterize the difference between various types of rotifers and to be substituted for human
inspection. A set of features was introduced to make the identification depend only on rotifer’s shape despite its orientation, dimensions, and location. This study
concentrated on three types of rotifers: rotifers without egg, rotifers with one egg, and rotifers with two eggs. Functions on the developed system included identifying,
counting and then recording the number of rotifers which carried the eggs automatically.
2. Materials and methods
2
.
1
. Sample preparation The rotifer Brachionus rotundiformis was reared in the laboratory culture tanks at
Taiwan Fisheries Research Institute, Tungkang, Taiwan. Different feeding condi- tions were investigated in this study Table 1. About 100 – 200 ml well-cultured
samples were collected below the water surface of the culture tank and 1 ml of sub-sample was taken from each of these samples using a 1-ml pipette and slightly
stirred simultaneously. The 1 ml sub-sample was discharged into a clear 75 × 25mm
2
glass slide with a blockade built around to prevent water overflow. In order
to make the microscopic observation easier, the sub-sample was added with 0.05 ml of 1 iodine solution to kill and stain the rotifers. This procedure let the rotifers
sprawl under water so that we could examine their eggs clearly. In order to avoid the objects from entanglement, the dense rotifer specimen was diluted repeatedly
using 1:1 clean seawater until the objects became separated. The number of rotifers in dense specimens could also be estimated by inverted trace of the dilution
operations.
2
.
2
. System description Fig. 1 illustrates the automatic processing system for classifying and counting
rotifers. The system consists chiefly of two units: a pattern recognition unit and a motion control unit. A microscope with 40 magnification was necessary for the
clear observation of rotifers. The microscope was equipped with a CCD camera to grab the rotifer images. Before starting the automatic system, a slide containing
certain sub-sample was carefully placed on a moving X-Y table. The X-Y table of the control unit was designed for moving the slide step by step like moving on
certain virtual grids, i.e. it could hold during image processing and move to next grid when the process was finished. The function of the pattern recognition unit was
to capture the image of grids and send it to the computer for image processing. After the image processing, the computer sends a signal to activate the motion
controller for moving the X-Y table forward for next process. This paper focuses on the pattern recognition unit which was the most important kernel when the system
was designed.
2
.
3
. Image processing In image segmentation, a region is defined as a group of spatially connected
pixels. A region, when properly defined, corresponds to an object. As shown in Fig. 2, proper regions disjointed from one another were screened for the discrimination
model. Each region was a candidate for extracting corresponding features for pattern recognition. An essential issue for invariants with the properties of rotation,
Table 1 Samples for testing and verification
Rotifer with Debris
Density estimation Specimen No.
Feeding Date
individualsml carried eggs
2 1
SP-1 96
090299 36
37 Tetraselmis chui
203 34
242 75
SP-2 15
100299 Chaetoceros affinis
375 43
Nannochloropsis oculata 66
65 213
35 100299
379 SP-3
Fig. 1. Main units of the automatic processing system.
scaling, and translation invariance RST invariance was introduced as well in this study. The RST invariants indicate that the features of objects are invariant in
terms of rotation, scaling, and translation. The extracted features should be RST invariants, because the concerned individuals were classified by their similarity
regardless of their orientation, size, or position.
The pilot image processing is drawn schematically in Fig. 3. Since the specimen was brown due to the iodine, the red channel component was more significant than
the other two components, both green and blue channels, in the standard RGB color model. The image in the red channel component was acquired and was
quantized into a 256-gray-level image.
A proper image threshold is required for transforming the gray scale image into a binary image. Exact threshold value is difficult to determine since the image
darkness depends on the concentration of iodine. Constant iodine concentration is not easy to control. However, moment-preserving thresholding algorithm proposed
by Tsai 1985 is a robust approach for determining the threshold value. In this study, they changed within a gray scale range of 180 – 200 when the red channel
image was used. The binary image after thresholding is shown in Fig. 2. An illustration of rotifers with varying number of eggs is also shown in Fig. 2. Three
Fig. 2. Rotifer images obtained from a microscopic observation: a without debris; b with debris, marked by a pointer. Where: 1-rotifer without eggs; 2-rotifer with one egg; 3-rotifer with two eggs;
4-debris.
types of rotifers were obtained from the microscopic observation: rotifers without egg, rotifers with single egg, and rotifers with two eggs. In this study, rotifers were
classified into the exact types in spite of debris that came from the sludge in the degraded water or from spoiled rotifer carcasses.
The requirement of the quality of images was important as they related to the image processing techniques. In degraded images, rotifers usually appear with many
Fig. 3. Flow chart of pilot image processing.
Fig. 4. Region modification for filling up rotifer’s interior: a original region in gray scale; b original region in binary; c region with morphological closing; d region refilling after closing.
trivial objects. The trivial objects are regions that can be separated easily before the discrimination model is applied. In order to maintain the images in a constant
quality, we used size to exclude some trivial objects, which were unquestionably not rotifers. The exclusion also reduced the calculation time and misclassification rates.
This study confined the objects of interest from 2,200 to 12,500 pixels for further identification.
Interested regions were extracted separately by a technique of labeling eight-con- nected components in the binary image. The regions were originally extracted in the
gray scale Fig. 4a and in the binary Fig. 4b. They have rugged borders, especially in the area close to corona as marked in Fig. 4b. Different processes
were performed to produce smooth border on the smooth region. Fig. 4 also shows the results from two processes: morphological boundary closing Fig. 4c as well
as region refilling after closing Fig. 4d. The images with morphological boundary closing using a 3 × 3 structuring element of 1’s were used for further
analysis.
2
.
4
. Moment in6ariants The pattern recognition technique of moment invariants was appropriate to
distinguish rotifers from debris because they were quite different in their shapes. Many techniques are available for shape description. If the situation in which the
rotifer under observation appear in any position or orientation, or in different sizes is considered, a shape analysis technique with RST invariance is required. Moment
invariants are really suitable for such requirements. They have frequently been used in several researches for shape recognition Gupta and Srinath, 1987; Leu, 1991;
Wen and Lozzi, 1993; Shen et al., 1994; Yang and Albregtsen, 1996. Moment invariants are important due to their special properties associated with their RST
invariance Hu, 1962; Gonzalez and Woods, 1992; Wood, 1996.
Hu has introduced the theory of moments of inertia to establish a set of seven shape moments with RST invariance derivation is shown in Appendix A.
f
1
= h
2,0
+ h
0,2
f
2
= h
2,0
− h
0,2 2
+ 4h
1,1 2
f
3
= h
3,0
− 3h
1,2 2
+ 3h
2,1
− h
0,3 2
f
4
= h
3,0
+ h
1,2 2
+ h
2,1
+ h
0,3 2
f
5
= h
3,0
− 3h
1,2
h
3,0
+ h
1,2
[h
3,0
+ h
1,2 2
− 3h
2,1
+ h
0,3 2
] +
3h
2,1
− h
0,3
h
2,1
+ h
0,3
[3h
3,0
+ h
1,2 2
− h
2,1
+ h
0,3 2
] f
6
= h
2,0
− h
0,2
[h
3,0
+ h
1,2 2
− h
2,1
+ h
0,3 2
] + 4h
1,1
h
3,0
+ h
1,2
h
2,1
+ h
0,3
f
7
= 3h
2,1
− h
0,3
h
3,0
+ h
1,2
[h
3,0
+ h
1,2 2
− 3h
2,1
+ h
0,3 2
] −
h
3,0
− 3h
1,2
h
2,1
+ h
0,3
[3h
3,0
+ h
1,2 2
− h
2,1
+ h
0,3 2
] 1
Reddi 1981 showed that Hu’s moments could be expressed in terms of radial and angular moments. Subsequently, Li 1992 used radial and angular moments in
a general way to derive invariant functions Appendix B. By applying binomial theorem to the radial and angular moments, generalized shape moment functions
were obtained. The conceptual importance of Li’s research eliminated the phase angle effect by multiplying the generalized functions using the complex conjugates
to derive invariant functions of arbitrary order. The invariant functions might reconstruct Hu’s moments. Moreover, they might derive higher-order moments.
Since the order of Hu’s moments was not enough to classify the rotifers in our study, higher-order invariants were introduced. The higher-order invariants will
result in higher sensitivity. Proper invariants, the order p + q of h
p,q
is less than or equal to 4 in this paper, are adopted to construct a describing space for rotifers. In
addition to Hu’s moments f
1
– f
7
, invariants f
8
– f
12
were added adequately for further analysis.
f
8
= h
4,0
+ h
2,2
+ h
0,4
f
9
= h
4,0
− h
0,4 2
+ 4h
3,1
+ h
1,3 2
f
10
= h
4,0
− 6h
2,2
+ h
0,4 2
+ 16h
3,1
− h
1,3 2
f
11
= h
4,0
− 6h
2,2
+ h
0,4
h
4,0
− h
0,4 2
− 4h
3,1
+ h
1,3 2
+ 16h
4,0
− h
0,4
h
3,1
+ h
1,3
h
3,1
− h
1,3
f
12
= h
4,0
− 6h
2,2
+ h
0,4
h
4,0
− h
0,4 2
− 4h
3,1
+ h
1,3 2
− 16h
4,0
− h
0,4
h
3,1
+ h
1,3
h
3,1
− h
1,3
2 The order of p
+
q for f
1
– f
12
is listed in Table 2. Notice that the order of f
1
– f
12
did not follow the sequence of their indices i.
2
.
5
. Two-stage discrimination model A two-stage model was built to identify the input patterns. First, debris was
dropped out of the class for interested regions. Secondly, the outcomes rotifers from the first stage were classified into three groups.
2
.
5
.
1
. Separation of debris from rotifers Several ways have been evaluated in our study to separate the debris from
rotifers. The debris might be the spoiled carcasses of rotifers or the sludge in degraded water. In general, debris do not have any regular form: some appear to
have significant visible differences from rotifers and others are similar to rotifers in shape. It makes debris separation more difficult than rotifer classification. To solve
this problem, two feasible ways are introduced in this paper, one is similarity measurement approach and the other is a degree of membership approach using the
foregoing shape moment invariants.
2
.
5
.
1
.
1
. Similarity measurement approach. The shape moment invariants f
1
– f
12
are features for discrimination which construct a multidimensional discrimination
feature space V. Using the distance of moment invariants to measure the similarity between two objects in V, we could decide which class the objects belonged.
Assuming the two feature vectors as:
F
i
= [f
i1
,f
i2
,...,f
in
]
T
, F
j
= [f
j 1
,f
j 2
,...,f
jn
]
T
.
Table 2 Order p+q for f
1
–f
12
6 4
12 8
2 Order p+q
f
6
f
3
f
2
f
5
f
1
Moment invariant f
8
f
4
f
9
f
7
f
10
f
11
f
12
Fig. 5. Debris R
D
separated from rotifers in terms of R , R
1
, and R
2
. Here: V is the whole feature space. f
i
and f
j
are arbitrary features in V. R , R
1
, and R
2
are the class scopes of rotifers with eggs 0, 1, and 2, respectively, in V, and R
D
is the class scope of debris.
The similarity measure of these two vectors was defined by F
i
− F
j
=
n k = 1
f
ik
− f
jk 2
12
. 3
One hundred and eighty-five rotifer samples, including 96 without eggs, 63 with single egg, and 26 with two eggs have been investigated for the centers and radii of
class scopes in V mean points for centers and average length for radii. Test samples with their features appeared as points in the feature space. Points located
within a region were classified to their corresponding classes. In practice, the rotifer class regions in V have been found to be overlapped each other. A simplified
two-dimensional plot is shown in Fig. 5, where f
i
and f
j
are chosen arbitrarily from f
1
– f
12
. As shown in Fig. 5, from the points in the overlapped portion, it was not easy to determine the class they belonged. Hence, similarity measurement is not
so good to be applied to distinguish rotifers. Nevertheless, it is still appropriate to separate debris R
D
from rotifers in terms of R , R
1
, and R
2
. Points outside the boundary of the union region are obviously regarded as debris R
D
. Points inside the union region of R
, R
1
, and R
2
are considered as rotifers.
2
.
5
.
2
. Degree of membership approach A degree of membership approach was proposed for comparison with the
method of similarity measurement for debris separation. The peak-like distributions are based on the probability histograms of a moment invariant f
i
for different regions, R
, R
1
, R
2
, and R
D
, mentioned in the previous section Fig. 6. Here, f
i
is chosen arbitrarily from f
1
– f
12
. The membership for each region appeared from its corresponding probabilities with respect to a specific f
i
. For example, a test sample which has a value x on the f
i
-axis in Fig. 6 can yield the probabilities degrees of membership P
x,R
, P
x,R
1
, P
x,R
2
, and P
x,R
D
corresponding to classes R , R
1
, R
2
, and R
D
respectively. Since P
x,R
is zero, the sample is not certainly classified as class R .
Using the magnitudes of these non-zero values, P
x,R
1
, P
x,R
2
, and P
x,R
D
, we can determine the corresponding class of the sample. When P
x,R
1
or P
x,R
2
is greater than their specified threshold T
R
1
or T
R
2
, the sample with value x can be determined as the member of R
1
or R
2
instead of R
D
.
Fig. 6. Schematic diagram to illustrate the degree of membership approach, where: definitions of f
i
, f
j
, R
, R
1
, R
2
, and R
D
are the same as in Fig. 8. An input value x is given, particular probabilities degree of membership P
x,R
, P
x,R
1
, P
x,R
2
, and P
x,R
D
corresponding to classes R , R
1
, R
2
, and R
D
would be obtained from the distribution curves. T
R
1
and T
R
2
are specified thresholds for membership determina- tion.
2
.
5
.
3
. Classification of rotifers The features extracted from rotifer patterns constituted the basis for classifica-
tion. To develop an effective model with the features, an accurate classification is important. In pattern recognition field, there are several ways to construct such a
model. A stochastic model using Fisher’s discrimination function had been evalu- ated. Since the accuracy was relatively less, they are not quite suitable for the
classification of rotifers. Artificial intelligent approaches were considered more suitable than stochastic approach, because of the complicated correlation between
three types of rotifers. Therefore, an artificial neural network ANN was chosen because of its effectiveness on sophisticated classification problems. The ANN uses
a non-algorithmic black box strategy to form a model by supervised or unsuper- vised training. The ANN has the advantage of solving problems in higher dimen-
sional feature space, especially, complex interactions among features. Fig. 7 shows the basic element of a neural network which is called a neuron. Let the moment
invariants such as f
1
, f
2
, …, f
12
be input variables. As shown in Fig. 7, the
Fig. 7. The processing element in an ANN: a model of neuron; b example of transfer function.
Fig. 8. The significant procedures for discrimination.
transformation of a linear combination of input variables with their weights and biases by a transfer function f produces the neuron output y:
y = f
n i = 1
w
i
·x
i
− u 4
where x
i
, input variables; w
i
, weights of input variables; u, bias; and y: neuron output.
Several types of transfer functions have been developed. Choice of the transfer function depends upon applications. A typical sigmoid non-linear transfer function
is shown in Fig. 7b. The ANN consists of a large number of highly inter-connected processing
elements neurons. It is therefore more robust than the other methods in dealing with complex problems. The most frequently used ANN is a back propagation
neural network BPNN. The BPNN is a typical supervised neural network whose learning rules are to keep adjusting the weights and biases of the network to
minimize the sum of squared errors of the network. The minimization is done by continually changing the values of the network weights and biases in the direction
of the steepest decent with respect to the sum of errors. This is called a gradient descent procedure. Changes in each weight and bias are proportional to element’s
effect on the sum-squared error of the network. Eventually, we use these weights and biases when the training finished to build the classification model for rotifers.
3. Results and discussion
