cICIC International ⃝2021
ISSN 1881-803X

ICIC Express Letters
Volume 15, Number 7, July 2021

pp. 755–762

NONCONTACT METHOD FOR ESTIMATING ELLIPTICITYAROUND THE GIRTH OF A FREE-RANGING DOLPHIN
Hiromitsu Hama1 and Tadamichi Morisaka2
1

Graduate School of Engineering
Osaka City University
3-3-138, Sugimoto, Sumiyoshi-ku, Osaka-shi 558-8585, Japan
hama@osaka-cu.ac.jp
2

Cetacean Research Center
Graduate School of Bioresources
Mie University
Room #619, 1577 Kurimamachiya-cho, Tsu City, Mie 514-8507, Japan
chaka@bio.mie-u.ac.jp

Received November 2020; accepted January 2021
Abstract. In recent years, wild dolphins that live in coastal areas that overlap withareas of human activity are being greatly aﬀected by the increasing conﬂict with humanactivities. Therefore, their growth rate and nutritional status must be monitored to aid
in their conservation. A method of measuring them has not yet been established, andresearch has not progressed. Therefore, we aim to develop the elemental technologies
necessary for constructing such a system, which would contribute to the health diagnosisof wild dolphins. This paper proposes a novel method to estimate the ellipticity aroundthe girth of free-ranging wild dolphins, and clarify their growth and leanness. The purpose of this study is to help conserve the dolphin population by capturing changes overtime.
Keywords: Dolphin conservation, Free-ranging, Leanness, Non-contact, Ellipticity estimation, Approximate parabola

1. Introduction. Anthropogenic activities, e.g., underwater construction, dredging, heavy ﬁshing, recreational activities at the shore, shipping, and traﬃc, have serious impacts
on wild aquatic animals, including dolphins, by destroying their natural habitats, decreasing their food resources, and increasing anthropogenic noise in the habitats [1]. To
conserve wild dolphins, their health must be constantly monitored.
For animals, even for humans, the body length and girth are important criteria thatindicate the health condition (especially the nutritional status), as well as the reproductivestatus (e.g., the body length is related to sexual maturity, and the pregnancy status canbe determined by the girth). Thus, these parameters are important basic information formonitoring the health condition of a population [2].
However, it is extremely diﬃcult to measure these parameters in free-ranging wild dolphins underwater. Therefore, researchers heavily rely on dead and/or stranded dolphinsfrom the population to measure the body length and girth [3]. Some research teams
catch dolphins to determine their health conditions [2]; however, this method is expensive
and places immense stress on the dolphin. Consequently, noninvasive methods to measure a dolphin’s length and girth are eagerly anticipated. We have already developed anoninvasive system for measuring the body length of free-ranging wild dolphins [4].
A noninvasive girth measurement for wild cetaceans (whales and dolphins) is rare.
Recently, Christiansen et al. [5] presented a method to obtain the girth of large whales by
DOI: 10.24507/icicel.15.07.755

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ﬁtting ellipses to the whale’s body in drone-video footages, and thereby estimated their
total body weight. They estimated the ellipse height and width based on the lateral anddorsal sides of the whale. This method can be applicable to slow and parallel-surfacing
large whales; however, it is diﬃcult to adapt for quick and bent-surfacing smaller dolphins.
In this paper, we propose the new method necessary for constructing a system to estimate the ellipticity of a cross-sectional view around the girth of individual wild dolphins.
The “leanness” criterion can be obtained without contact, using a video camera with
underwater housing or water-resistant video camera. When monitoring wild animals overa long period, the system should be compact and easy for anyone to handle and use [6].
Then, the changes in the nutritional state of the population could be observed over timeby monitoring the girth of wild dolphins without causing them any stress.
2. Proposed Method.
2.1. Overall block diagram. Figure 1 shows the overall block diagram. First, videos
of free-ranging dolphins were taken using an underwater video camera. As a precaution,
it was supposed that the dolphin’s body axis and the camera’s optical axis are almost
perpendicular to each other, and the dolphin is rotating around its body axis. Next,
the video frames that meet the conditions were extracted from the obtained video. The
still images were captured, and the dolphin areas were extracted. The lengths of the line
segments were then measured, as described later in text.

Figure 1. Overall block diagram for estimating a dolphin’s leanness
Since the unit of measurement can be pixels on a monitor screen or centimeters on asheet of printed paper, this plays a role of normalization in postprocessing. This increases
the processing ﬂexibility and eases the system usage. Furthermore, ellipticity α wasobtained using our proposed formula, after which, normalized parameter β was achieved
and output as the leanness criterion.
2.2. Definitions and symbols. The counter lines of the cross section around a dolphin’s
girth can be well approximated by an ellipse [5]. This aspect is shown by the dashed lines
in the images on the left side of Figure 2. Dolphins and whales are cetaceans and have
similar body structures; hence, this fact may be applicable to dolphins. In fact, thedeveloped method is applicable not only to dolphins but also whales, as a weight index.

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Figure 2. Ellipse approximation and parameters on a dolphin cut plane [7]This section describes a method for determining the ellipticity, supposing that the crosssection of a dolphin is elliptical.
Let us ﬁrst deﬁne some symbols, as measured at the tip of dorsal ﬁn:
W : Width (perpendicular to the body axis through the anterior origin of the dorsal ﬁn).
W1 and W2 : Lengths of the line segments on the left and right sides of the dorsal ﬁn,
respectively:
W = W1 + W2 .
(1)∆: Distance between the center of the width and anterior origin of the dorsal ﬁn:∆ = W/2 − W1 = W2 − W/2.

(2)

α: Ratio of the length of the minor axis to that of the major axis of an approximatedellipse:α = 2a/2b (a < b). α = a, when b = 1, (Ellipticity).
(3)
β: Ratio of the values of W when ∆/W = 0.4 (W0.4 ) and when ∆/W = 0 (W0 ).
These aspects are shown on the right side of Figure 2, and the aspect of β will be shown
later in Figure 4. α and β are important parameters, as explained in Section 3, and canbe derived from ∆ and W through mathematical calculations (see the Appendix for thederivation). β is used as the leanness criterion:(()(1/2) ) /β = 9 + 16 × α25.
(4)Here, β is obtained by W0.4 /W0 , where W0.4 = W (∆/W = 0.4) and W0 = W (∆/W =0). In this study, β = 0.4 because it is possible to experimentally obtain values up
to this level, in most cases. A value of 0.5 or more is diﬃcult to obtain for a moving
dolphin. In addition, α could be obtained from an inverse quadratic function. If weuse the approximated inverse function, β may be easier to obtain. The proposed system

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H. HAMA AND T. MORISAKAworks well when the optical axis of the video camera is perpendicular to the body axis.
However, the captured still images should be clear and distortion-free.
2.3. Experiments. The eﬀectiveness and high ﬂexibility of the proposed method wereconﬁrmed through mock experiments using hand-made elliptical paper cylinders [E] anda real video of a dolphin [R]. [E], [R], and [E, R] indicate the use of the former one, thelatter one and both, respectively. The experimental process is as follows.
[E] [Construction of elliptic cylinders.] At this time, it is diﬃcult to determine α;
therefore, we ﬁrst constructed elliptic cylinders with the appropriate ellipticities. Then,the values could be obtained by measuring α: α ∈ {0.935, 0.765, 0.653}.
[E] [Shooting: Elliptic cylinder photographs.] We continuously shot still images whilerotating the elliptic cylinders every ﬁve degrees. Because high accuracy is not required,the rotation angle may be appropriate. We extracted an elliptic cylinder from the images
and its parameters; see Figure 3(a).

(a) Examples of rotated images of an elliptical cylinder(b) Examples of dolphin images captured from a real video (Rotatingaround the body axis)

Figure 3. Examples of two experiment types used for algorithm evaluation[R] [Shooting: Video of a dolphin.] We shot a video of a dolphin in the free-ranging
state. The restraint conditions at the time of shooting are as follows. 1) The dolphin’s
body axis should be perpendicular to the camera’s optical axis. 2) The rotations must be
around the body axis. Then, we selected the frames suitable for restoration, cut out thedolphin, and extracted the parameters; see Figure 3(b).
[E], [R] [Selection and cutting out of dolphins to be analyzed.] We measured the lengthof the feature line segments, W1 , W2 , and W (any unit (cm, pixels) is acceptable, seeFigure 2).
[E], [R] [Parameter calculation, graph: (x, y) = (∆/W, W ), y = f (x).] We added symmetric data with respect to ∆/W (x axis) (x = −∆/W ). When we drew an approximate
parabola, the ﬁrst-order coeﬃcient was desired to be extremely close to 0. Because it issymmetrical with respect to the y axis, we deﬁne the new W (x) = f (x) + f (−x); then,W (−x) = W (x).
[E], [R] [Acquisition of α and β.] α was obtained by the proportional distribution fromthe reference graph calculated in advance. β was calculated using Equation (5). Both αICIC EXPRESS LETTERS, VOL.15, NO.7, 2021

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and β can be indicators of leanness; we normalized them by dividing by f (0) to eliminate
the diﬀerence in the distance between the camera and dolphin (Distance-Invariance).
g(x) = f (x)/f (0);β , g(0.4)(5)

Only the six images in Figure 3(b) were used for restoration. The necessary equipment
includes an underwater video camera and a personal computer. As such, we obtained
α = 0.88 and β = 1.08. Although there is room for improvement in accuracy, we conﬁrmedthat it is possible to estimate the ellipticity of the cross section. This is the basis for thenoncontact leanness estimation.
3. Experimental Results Using Elliptic Cylinders and Real Video Frames. Experiments were performed according to the procedure described in the previous section.
Figures 4(a) and 4(b) show the results. In Figure 4(a), the horizontal axis (x) represents ∆/W , and the vertical axis (y) represents W (the central axis) and ∆ (the rightaxis). Good approximations of W and ∆ were obtained through quadratic and linear
equations, respectively. The approximate curves are represented by dotted lines. When(a) Relations among x = ∆/W , y1 = W , and y2 = ∆(b) Evaluation measure after normalization

Figure 4. Relations between each parameter (Horizontal axis: ∆/W , Major axis = 2)

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unknown data are obtained, they can be calculated by overlaying them on this graph andproportionally distributing them.
Figure 4(b) shows the normalized curves, g(x), as shown in Figure 4(a). As a reference,the curves corresponding to α ∈ {0.6, 0.7, 0.8, 0.9}, obtained by calculation in advance,
are shown by dashed lines. The results of the mock experiments and a child dolphin are
shown by other line types, corresponding to α ∈ {0.653, 0.765, 0.965}. This graph showsthat the results of the mock experiment are just within the corresponding range of thetheoretically obtained graph. As described later, the numerical values were obtained withfairly good accuracy.
Figure 4(b) shows that β = g(0.4) may be used as the leanness criterion (overweightand underweight). The larger the value of β, the leaner the dolphin, and the smaller itsvalue, the fatter the dolphin. Distance-invariance was realized using Equation (5). Thisis an important concept, which could indicate the application of the system, regardless ofthe distance between the target and camera.
The eﬀectiveness of the proposed method was conﬁrmed using video frames of a real
dolphin. The true values of the actual dolphin are unknown; they could not be evaluated.
However, β = 0.884 seems to be a reasonable value. These values are listed in Table 1,along with the estimated values of α and β obtained through experiments, in which theeﬀectiveness of introducing β can be conﬁrmed. Figure 5 shows a good approximation
between the mock experiment (solid line, marker •) and the theoretical value (dashedline, marker N) used as a reference.
Table 1. Estimation of α and β and evaluation of error
α1
β1

0.6
1.350

Reference
0.7
0.8
1.239
1.145

0.9
1.067

Elliptic cylinders
Dolphinα0.653 0.765
0.935
(*)
β1.285 1.172
1.043
1.078
α′0.661 0.780
0.915
0.878
Error′
α − α 0.008 0.015 −0.020−
1.21% 1.92% −2.19%−(*) True value unknown

Figure 5. Two nearly equal lines

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4. Conclusions. Surprisingly, it has been diﬃcult to ﬁnd 3D models of dolphins thatare strictly taken from measurements of real dolphins. Even if a computed tomographyscan on land is used, the abdomen will be dented, owing to gravity. If we can measurethem properly in water, the technique can be applied to various studies. Because theproposed method is applicable to free-ranging wild dolphins, such weak points could beovercome. Because the cross section of a dolphin can be well approximated by an ellipse,
an inexpensive and simple system could be constructed by using one video camera andone PC.
In the future, true values of the girth of free-ranging dolphins could be obtained and veriﬁed using more real images, and improving the robustness and stability of the algorithm.
When multiple video cameras are used, we can eﬀectively obtain more suitable images
and more accurate results. The results of our experiments conﬁrmed the eﬀectiveness andﬂexibility of the proposed method.
Acknowledgements. This work was supported by a Grant-in-Aid for Scientiﬁc Research(C), JSPS KAKENHI Grant Number JP18K05782. We are grateful to Mr. Kazunobu Kogi
(Mikurashima Tourist Information) and Dr. Mai Sakai (Kindai University) for providing
videos of wild dolphins in Mikura Island, and Ms. Yukie Hashimoto (Otemon GakuinUniversity) for helping with preliminary experiments in Excel. We would like to thank
Editage (www.editage.com) for English language editing.
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Appendix. Calculation of α from W and ∆.
If the ellipse with a 2a minor axis and 2b major axis rotates θ degrees, the (x′ , y ′ ) of
the original ellipse can be explained through the following formula by using the (x, y) of
the rotated ellipse (see Figure 6):x′ = x cos(−θ) − y sin(−θ) = x cos θ + y sin θ = a cos β,y ′ = x sin(−θ) + y cos(−θ) = −x sin θ + y cos θ = b sin β,()(1/2)× sin(β + γ) (−180◦ 5 γ 5 180◦ ) ,x = a2 cos2 θ + b2 sin2 θ(6)(7)(8)

where −1 5 sin(β + γ) 5 1, then()(1/2)min(x) = − a2 cos2 θ + b2 sin2 θ,

(9)

762

H. HAMA AND T. MORISAKAThen,()(1/2)
max(x) = a2 cos2 θ + b2 sin2 θ.

(10)()(1/2)
W = 2 × a2 cos2 θ + b2 sin2 θ.

(11)Now,(())(1/2)∆ = b sin θ, and a = b × α; then, W = 2 × (b × α)2 + 1 − α2 × ∆2.

Then, we obtain∆/W0 = 0, ∆/W0.4 = 0.4; then, β = W0.4 /W0 =((9 + 16 × α2Figure 6. Calculation of α from W and ∆)(1/2) )/5.

(12)(13)