A simple laser photogrammetry technique for measuring Hector's dolphins (Cephalorhynchus hectori) in the field



The ability to measure and age individuals within a population has many important applications, for example, for examining growth and determining size class. We developed a simple photogrammetric system using two parallel lasers and a digital camera, in order to measure dorsal fin dimensions of free-ranging Hector's dolphins. Laser dots were projected onto the fin, providing scale, thus allowing measurement as well as simultaneous photo-ID of 34 individuals from fin nicks and other marks. Multiple measurements (≥5) were available for six individuals; these resulted in mean CVs of 3.71% for fin length and 3.76% for fin height. Errors due to variations in angle and measurement were quantified via photography of a fiberglass Hector's dolphin model. Allometric measurements and age data were collated from 233 autopsied Hector's dolphins. Using these data, fin length was found to be a better predictor of total length (females r2= 0.732, males r2= 0.678) than fin height. Gompertz age/length growth curves were fitted to these individuals. Linear regressions were used to estimate total length for 34 individuals from laser-metrically estimated fin base length. Individuals were then assigned one of three age categories. This system shows promise as a noninvasive way of measuring individuals, while allowing simultaneous photographic identification.

The ability to age and measure individuals within a population is useful for a variety of reasons. Length estimation is important for examining growth (Clark et al. 2000), determining size class (Cubbage and Calambokidis 1987), subspecific status (Baker et al. 2002), different geographic forms (Perryman and Lynn 1993, Perryman and Westlake 1998, Jaquet 2006) and the extent of sexual size dimorphism (Ramos et al. 2002, Martin and Da Silva 2006). Age estimates are required for age-structured population models (Slooten and Lad 1991, Cameron et al. 1999). Age and size also determine maturity and influence reproductive success (Martin and Rothery 1993).

It is difficult to calculate exact ages for marine mammals; however, a number of techniques are commonly used to provide an estimate of age. The standard procedure for estimating age in odontocetes and pinnipeds involves counting the incremental growth layers in tooth sections (Perrin and Myrick 1980, Myrick et al. 1984). This technique has been used on live animals but is highly invasive as it involves capture of the animal and extraction of a tooth (Arnbom et al. 1992, Childerhouse et al. 2004, Bell et al. 2005). Long-term photo-ID studies can also provide age data (Hamilton et al. 1998), but this requires intensive fieldwork over the study species' lifetime and typically obtains a minimum age, unless the individual is marked as a calf (e.g., Kraus et al. 1986).

Photogrammetry is a well-established, noninvasive method for measuring individuals, both in terrestrial and marine environments (e.g., elephants, Loxondonta africana, Schrader et al. 2006; gorillas, Gorilla gorilla, Breuer et al. 2006; and northern bluefin tuna, Thunnus thynnus thynnus, Costa et al. 2006). Photogrammetric techniques are particularly useful as noninvasive field methods for marine mammals, as they do not require capture. There are two general approaches to photogrammetry, either stereo-photography or single camera photography. Stereo-photogrammetry uses a pair of overlapping images to create a 3-D optical model, in which scale is provided by the known distance between the cameras and the lens magnification (e.g., Ratnaswamy and Winn 1993, Dawson et al. 1995, Bräger and Chong 1999, Waite et al. 2007). Single camera photogrammetry requires either a known object in the image for scale (e.g., Best and Rüther 1992, Flamm et al. 2000) or a measurement of the range to the individual (e.g., Gordon 1991, Spitz et al. 2000, Jaquet 2006). A more recent development in single camera photogrammetry uses a pair of parallel lasers to provide scale in the images (Durban and Parsons 2006, Rowe and Dawson 2009).

A previous stereo-photogrammetric system was developed for Hector's dolphins to measure bowriding dolphins (Bräger et al. 1999). While stereo-photogrammetry is inherently more accurate than single camera systems, and 3-D measurements are possible, this type of system was cumbersome both in the field and during analysis. Also, their greater accuracy may be of little advantage when measuring animals that are flexible (Dawson et al. 1995).

Laser photogrammetry is a simple, single camera method that has previously been used to measure rockfish (Sebastes sp., Gingras et al. 1998, Yoklavich et al. 2000), to quantify and measure fish assemblages around oil platforms (Love et al. 2000), to measure a variety of fish species in the Bay of Biscay (Rochet et al. 2006) and to measure dorsal fin dimensions of orca (Durban and Parsons 2006). This method uses two parallel lasers mounted on a digital camera. The lasers project dots at a known distance apart in the photographic images, to establish scale and allow measurement of the dorsal fin. Further, the same images can be used in standard photo-ID, thus identifying and measuring individuals simultaneously. Growth curves and regressions constructed from dissection data can then be used to relate the dorsal fin dimensions to total length and age for Hector's dolphins.



Combined photo-ID and laser photogrammetric photographs were taken during boat surveys off the coast of Banks Peninsula, New Zealand, between December 2005 and February 2008. Photographs were taken from a 6 m, outboard powered research vessel. A Nikon D1H digital camera (Nikon Imaging Inc., Tokyo, Japan) with an 80–200 mm f2.8 zoom lens was used with two laser pointers set in a high-density nylon block secured to the tripod mount. The block mount was custom-made to fit the laser pointers, which were set at 10 cm apart and were adjustable for calibration. The lasers (Z-bolt model BTG-10, wavelength 532 nm, output power <5 mW) were eye safe, although direct eye contact should be avoided.

Each day before use, the lasers were tested at two different distances (2.3 m and 6.5 m) to check that they were parallel. These distances were chosen as they are within the typical range for Hector's dolphin identification photographs. In the field, photos were taken of the dorsal fin of any identifiable dolphins so that the laser dots were projected onto the fin or body (Fig. 1).

Figure 1.

Digital photograph of a Hector's dolphin dorsal fin with projected laser dots and dorsal fin measurements.

Each photograph was graded for quality to ensure that it had been taken from as close to side-on to the dolphin as possible, with laser dots clearly visible, with dorsal fin in focus and taken from approximately within the calibration range.

Dorsal fin height and dorsal fin base length were measured from the digital images using graphics software Intaglio v.2.9.3. The known separation distance of the lasers (10 cm) was used to calibrate the photographs. Measurement tools within the software were used to measure dorsal fin dimensions. Measurements of dorsal fin base length were taken from the midpoint of the curve at the anterior edge of the fin to the notch at the posterior edge of the fin along the base of the fin (Fig. 1). Measurements of dorsal fin height were taken by drawing a line parallel to the base of dorsal fin, which just touches the top of the fin, then extending a line perpendicular to the two parallel lines (Fig. 1).

Sources of Error

Several sources of error are present at all stages of this photogrammetric method, both in the field and during the measurement process. Errors in the field include those which occur during the photographing of individuals, due to the alignment of the lasers and those occurring naturally due to the flexing of individuals. Horizontal axis error, which occurs when the dolphin does not surface exactly side-on to the camera, and parallax error, which occurs when the photographer is looking down on the subject (Durban and Parsons 2006), both cause negative biases in measurements. Flexing of the dolphin's body may subtly change the shape and dimensions of the dorsal fin. Additionally, sensitivity of the nylon laser mount to temperature fluctuations may lead to alignment errors. In the field these errors were minimized by using the same photographer (TW), taking care that photographs were taken as close to perpendicular as possible, from ranges of approximately 2–6 m, and by calibrating the lasers daily. In analysis we discarded any images that were not sharp, poorly exposed, taken from too far away, or which appeared to be nonparallel.

Errors in the measurement process arise from three major sources: variability between observers, variability in measurement method and poorly defined metrics (or definition error). These were minimized by having the same person take all of the measurements, following a standardized set-up procedure.

It was not possible to estimate directly the magnitude of all errors involved in this photogrammetric method, as Hector's dolphins of known size are not available for comparison in the field. Instead, error reduction strategies were employed and indirect techniques were also used to quantify errors where feasible.

The combination of errors (except flexing) was measured by taking three replicate photographs of a fiberglass Hector's dolphin model at each of 5° increments between 0° and 55° from perpendicular to the model and at three different distances (2.5, 5, and 7.5 m). This was done because while some errors (e.g., horizontal axis error, parallax error) should be strictly trigonometric, other errors (e.g., definition error, alignment of lasers) may not be. Replicate measurements on the same photograph were not carried out in succession.

The precision of measurements taken from Hector's dolphins was quantified by measuring randomly chosen photographs of those individuals photographed multiple times. Here too, measurements were not carried out in succession. A model II analysis of variance (ANOVA) was used to partition the variance of dorsal fin measurements into “within” and “among” dolphins, and then calculate percentage measurement error. Measurement error is defined here as the variability of repeated measurements of dorsal fin dimensions taken on the same individual, relative to the variability of these dimensions among individuals (see Bailey and Byrnes 1990 for method),


Allometric Measurements

Measurement data from bycaught and stranded Hector's dolphins were collated from a number of different sources (Slooten 1991; Duignan et al. 2003, 2004; Duignan and Jones 2005). Measurements gained during autopsies by experienced researchers, and age estimates from counting GLGs in teeth (e.g., Slooten 1991), are assumed to be without error. A linear regression was fitted to dorsal fin height and dorsal fin length against total length. Von Bertalanffy (Von Bertalanffy 1938), Gompertz (Gompertz 1825) and Richards (Richards 1959) growth curves were used to describe growth. Growth functions of the following form were fitted using least squares estimation of the parameters in program JMP v5


where L is asymptotic total length (or fin height or fin length), t is age in years, k is a growth rate constant, b is the constant of integration, and M specifies the relative position of the asymptote.


Multiple photographs of a Hector's dolphin model examined a combination of errors and showed that deviations of up to 20° from perpendicular resulted in dorsal fin measurements within 2% of actual values. Over this range of angles, there were no obvious biases caused by variation in range (Fig. 2).

Figure 2.

Mean error in dorsal fin length measurements with angle from perpendicular.

The model II ANOVA using data from dolphins that had been repeatedly photographed and measured showed that the variation between individuals was far greater than the variation between multiple remeasurements of the same photograph. The results of the ANOVA were highly significant for dorsal fin height (F= 2,320.04, df = 32, 132, P < 0.001) and dorsal fin length (F= 2,216.87, df = 325, 132, P < 0.001). Percentage measurement error (see formula in Methods) was also minimal at 0.22% for dorsal fin height and 0.23% for dorsal fin length.

Ninety-five images of 34 identifiable dolphins showed projected laser dots, were sharply focused and showed ideal orientation of the individual to the camera. Twenty individuals were of known sex (12 females and 8 males). The number of photographs for each individual ranged from 1 to 19 (x̄= 2.88). Dorsal fin height ranged from 8.04 cm to 11.57 cm and fin base length was in the range from 17.10 cm to 23.76 cm.

Six identifiable individuals of known sex and known minimum age (calculated using photo-ID data) were photographed five or more times (including two individuals on different days, Fig. 3). These individuals show an increase in dorsal fin length with age, as expected. The mean CV of dorsal fin base length for these individuals was 3.71% (range 1.57%–5.71%) and for dorsal fin height was 3.76% (range 2.04%–5.86%).

Figure 3.

Variability in dorsal fin base length measurements for six individuals photographed five or more times. Minimum age and sex are given under the identifying number of each individual.

Allometric Measurements and Growth Curves

A total of 233 individuals with either two or more relevant allometric measurements, or estimated age (from GLGs) and one or more measurements were represented in the autopsy data. Ninety four percent of these dolphins were of known sex (127 males and 92 females) and 73.4% were of known age.

Von Bertalanffy, Gompertz, and Richard's growth models were fitted to autopsy data for total length, dorsal fin height, and dorsal fin base length for male and female Hector's dolphins separately. The Richard's growth model, typically, did not converge, and was therefore considered unreliable for these data. There was very little difference between Von Bertalanffy and Gompertz growth functions. Von Bertalanffy growth curves were a marginally better fit and had a slightly lower residual of the sum of squares. However, Gompertz growth curves fitted the lower end of the data (i.e., the younger animals) much better than Von Bertalanffy curves. Since this portion of the curve is most important for growth, Gompertz curves were chosen (Fig. 4).

Figure 4.

Gompertz growth curves for male and female Hector's dolphins.

Linear regressions showed that dorsal fin base length was a far better predictor of total length (females r2= 0.73, males r2= 0.69; Fig. 5) than dorsal fin height (females r2= 0.51, males r2= 0.58; Fig. 6). Females had a slightly better relationship between fin base length and total length than males (Fig. 5).

Figure 5.

Relationship between total length and dorsal fin base length for male and female Hector's dolphins. The regression relationship labeled “Unknown sex” is for all data including three individuals of unknown sex.

Figure 6.

Relationship between total length and dorsal fin height for male and female Hector's dolphins. The regression relationship labeled “Unknown sex” is for all data including ten individuals of unknown sex.

The regressions were used to estimate total length from data on dorsal fin base length for 34 individuals that were measured using the photogrammetric method. Gender specific linear regressions were used where possible. The estimated total lengths for females ranged from 115.8 cm to 143.1 cm. Males were slightly smaller between 97.1 cm and 126.0 cm. Individuals of undetermined sex had total lengths of between 110.9 cm and 137.1 cm.

It has not been possible to estimate age from photogrammetric measurements, for two reasons. Firstly, there is a great deal of variability in the body measurement data; for example, 2-yr-old males range from 90 to 120 cm. Also, the nature of these growth curves is that they plateau at approximately 5–6 yr. Thus a female ≥134 cm could be anywhere between 6 and 20 yr old. It was possible, however, to place laser-metrically measured individuals into broad age categories, based on their dorsal fin base length (Table 1). Age categories were determined using information on fin length measurements, estimated age (from tooth sections) and maturity status from the collated autopsy data.

Table 1.  Age categories determined by dorsal fin length for individuals of either known or unknown sex, and the number of individuals in each category (n).
 MaleFemaleUnknown gender
Juvenile≤18.2 cm≤19.2 cm≤18.2 cm
n= 2n= 0n= 0
Intermediate18.3–20.5 cm19.3–21.5 cm18.3–21.5 cm
n= 3n= 9n= 4
Mature≥20.6 cm≥21.6 cm≥21.6 cm
n= 1n= 3n= 4

Individuals that are either particularly large for their age or particularly small are difficult to age. An intermediate category (Table 1) encompasses these individuals as well as those of medium fin length that are unable to be assigned to either the juvenile or mature category.


The laser photogrammetric technique applied here was first tested on cetaceans by Durban and Parsons (2006) to measure the dorsal fin height of orca, and has since been used on bottlenose dolphins (Rowe and Dawson 2009). These systems are inexpensive, require very little equipment, and are easy to set up and use. Another major benefit is that identification photographs are obtained simultaneously.

This method resulted in a mean CV of 3.71% for dorsal fin base length and 3.76% for fin height, which compare favorably with other photogrammetric techniques for measuring cetaceans in the field. Stereo-photogrammetric measurement of blowhole to dorsal fin distance in sperm whales using a boat based technique yielded a mean CV of 4.38% (Dawson et al. 1995). An underwater videogrammetry method for obtaining lengths of humpback whales resulted in a mean CV of 3.08% for mothers and 2.57% for escorts (Spitz et al. 2000). Median CVs varied from 1.29% to 4.56% for various morphometric measurements of right whales (Best and Rüther 1992). A median CV of 1.3% was obtained for individual fluke measurements of sperm whales (Jaquet 2006).

Errors will never be completely eliminated from this photogrammetric system but they can be quantified and reduced where possible. Accuracy was demonstrated by photographing a life-size Hector's dolphin model of known dimensions. When the model was 20° from perpendicular to the camera, theoretically, parallax error alone would produce an error of 6%. However, a combination of errors are acting, some of which apparently counteract the parallax error, so that all measurements from the laser photogrammetric system were within 2% of the actual measurements. Similarly, a measurement technique applied to sperm whale flukes (Jaquet 2006) found that errors were small when the angle between the fluke surface and a plane perpendicular to the camera was <10° and that at angles >20° measurements do not provide reliable size estimates. Measurement errors (quantified via multiple, nonsequential, remeasurement of the same images) were low for this photogrammetric method (0.22–0.23%). Also, it should be remembered that because dolphins are inherently flexible, even a perfect system used repeatedly on the same individual would not produce exactly the same measurements.

Dorsal fin base length was found to be a better predictor of total length than dorsal fin height and hence was used to estimate length of living dolphins. Individual lengths calculated for these animals were within the known total length range for Hector's dolphins (Slooten 1991; Duignan et al. 2003, 2004; Duignan and Jones 2005).

Due to variation in body measurement data, age could not be predicted accurately from measurements of dorsal fin dimensions and growth curves. Broad age categories can, however, be assigned to individuals measured using the laser photogrammetric technique. This method therefore shows promise to provide field data that might be used, for example, in a stage-structured population model. This would avoid the need to use potentially biased age distributions gained from dead animals, the majority of which have been incidentally killed in gill nets (e.g., Slooten 1991).

We noted that the black mounting block sometimes became warm in the sun, and this may have affected laser alignment. Using white nylon material (instead of black) is advised. Also, we noted that the Z-bolt laser pointers that we used were not collimated, that is, the axis of the laser beam and the laser pointer's tubular body were not the same. We corrected for this during calibration, but in future would use higher quality lasers, in which this is adjustable.

The laser photogrammetric method trialed here has several potential future uses for marine mammals. The system is particularly useful for those species that are identifiable from nicks in the dorsal fin. Measurement of body proportions could potentially be applied to individuals to help determine health status and pregnancy in the field (e.g., Pettis et al. 2004). Age estimation using this technique and age-length data would be more effective in species that mature late and grow for much of their lives. Growth curves need to be examined beforehand and the relationship between a particular measurement and age needs to be tight for age determination to be effective. In order to establish growth curves with sufficient data points, a significant number of dead animals would need to be available for measurement. This may limit studies, for example, to species which mass strand or those with significant bycatch. Differences in length between subspecies could be detectable using this laser-metric technique, assuming that the difference in length is greater than the errors involved (e.g., common dolphins, Perryman and Lynn 1993; spinner dolphins, Perryman and Westlake 1998). The use of scale in identification photographs may elucidate the causes of identifying marks, for example, the examination of puncture wounds to identify predator species or scars from collisions with propellers in order to identify the type of vessel involved. Last, measurement data might be a useful adjunct in photo-ID, allowing discrimination of different sized individuals that bear similar marks.


This study was possible thanks to support and funding from the New Zealand Whale and Dolphin Trust. Thanks to Will Rayment for his assistance with data collection and Black Cat Group for logistical support. Many thanks to the Fraser family for their help and support at Banks Peninsula. The University of Otago Research Committee provided a University of Otago Postgraduate Publishing Bursary enabling the completion of this article. This manuscript was greatly improved by comments from Richard Connor, Will Rayment, and three anonymous reviewers.