Video analysis, part 2: water against optics

Part 1 concluded with two methodological claims: first, that underwater measurement accuracy depends less on sensor resolution than on the optical path of light and how the camera is calibrated for it; second, that underwater image quality is constrained primarily by the camera shutter and the aquatic medium itself. In Part 2, we substantiate both claims quantitatively.

The argument proceeds in three stages:

• First, we examine the physics of refraction across media boundaries and evaluate calibration methods: two-dimensional (2D) planar scaling and three-dimensional (3D) reconstruction using calibration frames, wand bundle adjustment, planar chessboards, and analytical air-to-water conversion.
• Second, we analyse hardware constraints: why consumer action cameras can achieve lower reconstruction errors underwater than in air, how two shutter mechanisms (exposure duration and rolling-shutter readout) degrade fast motion, and what geometric limits govern rigid stereo bars.
• Finally, we formulate a practical configuration protocol for poolside measurement and demonstrate how millimetre-level coordinate errors propagate into large errors in estimated hydrodynamic forces.

The physics of refraction: where the light bends

In every underwater filming configuration, a three-layer optical interface (water, glass, and air) separates the swimmer from the imaging sensor. Refraction across this interface introduces systematic errors into reconstructed spatial coordinates (Callaway et al., 2009), and the systematic review of swimming video methods lists refraction among the metrological limitations of video (Mooney et al., 2015).

Three hardware configurations can provide an underwater view, and the distinction between them reduces to where the refracting interface is positioned along the optical path (Mooney et al., 2015):

1. Waterproof housings. The most common and versatile poolside solution. Because the housing port sits immediately in front of the lens, the short distance between the camera’s optical centre and the refracting boundary induces substantial reconstruction errors unless explicitly modelled.
2. Submerged viewing windows. Built into the pool wall, viewing windows increase the camera-to-interface distance, but require specialised facility architecture and still refract incoming rays across the glass pane.
3. Periscopes. By keeping the camera unit above the surface while using mirrors to view underwater, periscopes allow simultaneous above- and underwater recording and maximise the camera-to-boundary distance, but require precision optics and carry a high cost.

The optical mechanism is identical to the familiar illusion of a straw appearing bent in a glass of water (Figure 1). A light ray originating from a submerged landmark changes direction as it passes from water through glass into air. Because a standard pinhole camera model postulates that light travels in straight lines through a homogeneous medium, it projects the landmark backward along the straight continuation of the refracted ray, rendering the apparent point shallower and laterally displaced from its true position. By Snell’s law, this angular deviation is zero along the normal to the interface (near the image centre) and increases nonlinearly toward the periphery. Furthermore, the wide-angle lenses that help image clarity underwater superimpose radial barrel distortion atop refractive bending (Callaway et al., 2009).

Text description

The figure takes two of the four cameras of Part 1’s Figure 1, in the same pool, at the same moments of the stroke and with the same picture of the swimmer, and shows each in two states: with straight rays (where the swimmer is), then as the light actually reaches the camera. In every state a section through the camera at true scale sits on top, the camera’s picture below it, and a few lines of figures beside the picture (under it on a phone).

1. Camera 1, above water, side. Position: on the deck, 0.9 m above the water and 6.75 m from the swimmer’s line; frame: the arm recovery. Section: the vertical plane through the camera and each of three points of the swimmer’s left hand under water (the elbow, the wrist and the fingertip), with the air, the water and the pool wall below the camera. Where he is: straight lines from the camera to the three points; the fingertip is 58 cm deep, the wrist 38 cm and the elbow 19 cm, and the picture shows the hand under water where it is. Where it sees him: each ray bends at the surface, steeply down in the water and almost level in the air; a dashed blue line continues the air leg straight on to where the camera places the point, a ring just under the surface: 9 cm deep for the fingertip, 6 cm for the wrist and 3 cm for the elbow, 48 cm off at the fingertip. In the picture the whole submerged body is squeezed into a thin band under the surface, and blue lines join each point to where it is seen.
2. Camera 3, under water, side. Position: on the side wall, 1.0 m below the surface and 6.1 m from the swimmer’s line, in a housing with a flat port 3 cm in front of the lens; frame: the catch. Section: the horizontal plane through the lens’ axis, seen from above, the half of it to one side of the axis: the camera at the wall and the swimmer’s lane line 6.1 m away. Where he is: the edge of the lens’ field reaches 2.23 m along the lane line, 4.47 m for the whole field; black points every 0.5 m along the line; the picture is Part 1’s view. A flat port 3 cm ahead: the light bends at the port; the real edge of the field (solid) covers only 3.26 m, while a camera calibrated in air still takes its edge ray to be the lens’ own (dashed), and so places every point along the line farther out than it is: by 17 cm at 0.5 m from the axis, 35 cm at 1 m and 60 cm at the edge (blue rings, with their errors). In the picture everything is magnified about 1.35 times; blue lines join points of a grid in the swimmer’s plane to where they are seen, growing from the centre of the picture outwards.

Animation sequence: the four states in turn, 3.5 seconds each: camera 1 straight and bent, camera 3 straight and through the port; readers who prefer reduced motion see the last.

How the pictures were made: in the refracted pictures every point under water is moved onto the line along which its light reaches the camera (Snell’s law, n = 1.333), and the same painting of the swimmer goes with it; their silhouettes match a ray-traced refraction of the same scene (overlap 0.98 for camera 1, 0.99 for camera 3).

Because refractive error is systematic rather than random, it can be mathematically modelled. To a first approximation, placing a camera behind a flat underwater port increases its effective focal length by a factor equal to the refractive index of water ($n\approx 1.333$), that is, by roughly a third. Empirical calibration of a GoPro Hero4 confirmed that its principal distance (the focal length parameter in the camera model) increased from 3.676 mm in air to 4.922 mm in water, a ratio of 1.34 (Shortis, 2015). This physical relationship was exploited directly in the study by Ceseracciu et al. (2011) discussed in Part 1: the authors calibrated their cameras in air and adapted the parameters to water analytically by multiplying the focal length by 1.333.

In short, the accuracy of any underwater calibration hinges on how faithfully its internal mathematical camera model accounts for the refractive medium in front of the lens.

Two-dimensional calibration: every plane requires its own scale

In two-dimensional (2D) video analysis, spatial scale is established by filming a reference object of known length (typically a one-metre calibration rod) positioned within the plane of motion (Mooney et al., 2015). As established in Part 1, a single camera preserves true scale solely within that calibrated plane. Underwater, this constraint becomes doubly strict because refraction deforms each plane differently. As shown by Kwon (1999; abstract only), refractive deformation in 2D underwater imaging is governed primarily by two variables: the camera-to-interface distance and the interface-to-object distance.

Consequently, a spatial scale calibrated at one depth plane is invalid for any other depth plane. Applied to a swimming pool, this yields a critical methodological rule: reference markings on the pool wall or on a lane rope lie outside the plane of a swimmer travelling down the centre of the lane and cannot provide an accurate scale. The calibration rod must be filmed through the identical camera and housing, positioned strictly along the swimmer’s line of travel.

The practical stringency of this requirement is demonstrated in a doctoral thesis that evaluated Dartfish underwater (Thow, 2016). Calibration was performed using two cables fitted with spheres at one-metre intervals (one suspended at the water surface and one at a depth of 1.5 m) stretched over the test lane and filmed through the recording cameras. Even with this setup, any measurement taken outside the calibration plane required explicit correction factors, including reference marks on the pool wall just 1 m farther away and frontal views in which spatial scale varied continuously with swimmer distance.

Three-dimensional calibration: the calibration frame

Classical three-dimensional (3D) calibration relies on a rigid calibration frame: a structure of known geometry bearing control points at precisely measured coordinates, filmed in the swimming lane prior to data collection. In the swimming literature, calibration frames have ranged in volume from 0.4 to 25.2 m³. A strict trade-off governs frame size: smaller frames yield lower spatial reconstruction errors, but restrict the volume within which the athlete can be measured. By convention, a reconstruction error below 5 mm per coordinate axis is considered acceptable for swimming biomechanics (Mooney et al., 2015).

What are the intrinsic limits of frame-based calibration? A study from the University of Porto demonstrated that increasing the number of control points improves accuracy only up to a ceiling (Figueiredo et al., 2011). An aluminium frame measuring 3 × 2 × 3 m was positioned half above and half below the water surface and recorded by four underwater and two above-water cameras. Direct linear transformation (DLT) reconstructions were computed using 8 to 30 control points across three spatial distributions. Reconstruction accuracy improved up to 20–24 control points, beyond which additional points yielded no further gain. The optimal layout reconstructed independent validation points with root-mean-square errors of 5.86, 3.45, and 4.38 mm along the three axes underwater, compared with 3.59, 3.11, and 4.00 mm above the surface.

Underwater errors were larger in most conditions (15 of the 21 combinations in the authors’ table, and at every number of control points in the best layout). The authors attribute this disparity to refraction: because linear DLT assumes rectilinear rays, the least-squares fit is forced to absorb refractive bending across the volume, producing the largest residuals near the boundaries of the frame. Two methodological corollaries follow:

1. Increasing the number of control points beyond roughly 20–24 provides no metrological benefit.
2. The swimmer must remain strictly within the boundaries of the calibration frame, as any movement outside the frame turns interpolation into unreliable extrapolation.

The decisive role of the calibration model in 3D

Holding camera hardware constant, the choice of mathematical calibration model can alter reconstruction error by an order of magnitude. Standard linear DLT ignores nonlinear optical distortions and refractive bending, which dominate underwater imaging.

The magnitude of this model effect was isolated in a series of controlled comparisons by Silvatti et al. (2012a, 2012b, 2013). Using the same pair of synchronised underwater cameras in waterproof housings and an identical validation test (700 frames of a rigid bar of known length swept across the working volume), the authors evaluated three calibration algorithms (Silvatti et al., 2012b):

1. Nonlinear DLT (standard DLT augmented with optical distortion terms): yielded a mean absolute error of 6.19 mm and a maximum single-frame error of 19.71 mm, with error magnitude varying significantly depending on where the bar was located within the volume.
2. Wand calibration with bundle adjustment: sweeping a calibration wand through the volume for 15 seconds and performing a simultaneous global optimisation of all camera parameters reduced the mean error to 1.16 mm (maximum error: 3.99 mm).
3. Planar waterproof chessboard: moving a rigid checkerboard grid slowly through the volume achieved a mean error of 0.73 mm (maximum error: 6.90 mm) (Figure 2).

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A chart (scale: 0 to 7 mm) comparing mean absolute 3D reconstruction errors across three experimental datasets. Each error is a fine line from zero ending in a dot; a dotted whisker runs on to the worst single error where reported; the rows filmed through water lie on a pale water tint. The head of each group names, in the accent colour, the factor between its two compared rows, which are drawn in the same colour:

• Group 1 — Vicon system with standard land calibration (Monnet et al., 2014); through the water × 8.8, from 0.65 to 5.75 mm:
  • In air, cameras surrounding the volume: mean error 0.19 mm (worst single error: 0.95 mm).
  • In air, cameras positioned behind pool viewing windows: mean error 0.65 mm (worst: 3.28 mm).
  • In water, filming through the viewing windows: mean error rises to 5.75 mm (whisker extends off-scale to a worst error of 16.69 mm).
• Group 2 — housed camera pair under three in-water calibrations (Silvatti et al., 2012b); by the method ÷ 8.5, from nonlinear DLT to the chessboard:
  • Nonlinear DLT: mean error 6.19 mm (worst error off-scale at 19.71 mm).
  • Wand + bundle adjustment: mean error 1.16 mm (worst: 3.99 mm).
  • Waterproof chessboard: mean error 0.73 mm (worst: 6.90 mm).
• Group 3 — GoPro pair with wand calibration (Bernardina et al., 2017); under water ÷ 1.6:
  • In air: mean error 0.97 mm.
  • Underwater: mean error 0.60 mm.

Animation sequence: the three experimental groups populate the chart sequentially from top to bottom, each line growing from zero to its dot, then the group’s factor.

Companion studies by the same group reinforce this finding: plain linear DLT produced spatially dependent errors ranging from 5.36 to 13.42 mm, whereas wand and chessboard calibrations remained below 3.65 mm uniformly across the volume (Silvatti et al., 2012a); in the subsequent journal publication (Silvatti et al., 2013; abstract only), classical DLT averaged 9.74 mm against 0.96 mm for the wand and 0.73 mm for the chessboard. Thus, with identical cameras in identical water, replacing DLT with bundle-adjusted wand or planar calibration shifts the error regime from roughly one centimetre (spatially variable) to about one millimetre (spatially uniform).

Could a high-end optical motion-capture system avoid these errors simply by remaining dry behind sub-surface viewing windows? Monnet et al. (2014) tested this directly using eight Vicon T-40 cameras (200 Hz) positioned in air outside the viewing windows of a laboratory pool, angled to minimise incidence angles across a compact 1.1 × 1 × 1 m volume. Calibration was performed using the manufacturer’s standard wand routine, which lacks a refractive model:

• With 10 cameras surrounding a dry volume in air (the manufacturer’s recommended geometry), mean absolute bar-length error was 0.19 mm (worst: 0.95 mm).
• With cameras arranged in the window layout (six to one side and two below), still filming in air, mean error was 0.65 mm (worst: 3.28 mm).
• When the rigid bar was submerged in water and filmed through the windows, mean error increased roughly ninefold to 5.75 mm (worst: 16.69 mm).

That 5.75 mm error is nearly identical to the 6.19 mm error of nonlinear DLT in housed cameras, leading the authors to conclude that the standard land calibration could be enhanced for through-window aquatic capture and that a planar chessboard calibration has to be tested.

Action cameras underwater: why water can outperform air

Can a consumer action camera serve as a precision measuring instrument underwater? Empirical testing demonstrates that it can: when calibrated directly in the water it films, a GoPro stereo pair achieved mean reconstruction errors below 3 mm across all tested recording modes, and down to 0.60 mm in its optimal mode (Bernardina et al., 2017).

Bernardina et al. (2017) positioned two GoPro Hero3+ Black cameras 2 m apart at a distance of 3.6 m from the test volume, synchronised via a flash. The identical geometrical setup was erected in a dry laboratory and underwater in a swimming pool, and calibrated in both media using wand bundle adjustment with lens-distortion terms matched to each field of view (FOV). Nine recording modes, combining three FOV settings (narrow 90°, medium 127°, wide 170°) with various resolutions and frame rates, were evaluated across 4,000 reconstructed lengths of a rigid bar.

The experiment established four principal findings:

1. Underwater versus air accuracy. Every configuration achieved a mean absolute error under 3 mm in both media, with the narrow FOV at 1920 × 1080 and 60 fps reaching 0.60 mm underwater. While the authors state in their text that underwater reconstruction outperformed air in all nine modes, inspection of their published data table shows that this holds for eight of the nine configurations; in the ninth mode (240 Hz), accuracy was nearly identical, with air marginally lower (2.76 mm underwater vs. 2.67 mm in air).

2. Physical mechanisms behind improved underwater accuracy. Two factors explain why submerging the cameras reduced error (Bernardina et al., 2017):

• Optical compensation of barrel distortion: Refraction across the flat housing port narrows the effective field of view and counteracts the severe fisheye distortion of the lens, reducing the fitted radial distortion coefficient (in the narrow FOV) from approximately −0.32 in air to −0.05 underwater.
• Target contrast: The black markers on the calibration wand exhibited higher visual contrast against the underwater background.

3. Non-transferability of air calibration. The bundle adjustment absorbed refractive effects by altering the estimated extrinsic parameters: although the cameras stood in the same arrangement, the algorithm computed the inter-camera baseline as 1945.5 mm underwater versus 2208.5 mm in air. Consequently, a camera pair calibrated in air cannot be deployed underwater without recalibration.

4. Trade-offs among camera settings (resolution and FOV vs. frame rate):

• Resolution outweighs frame rate: Modes operating at 1920 × 1080 and 60 Hz were the most accurate. The highest frame rate (240 Hz), which forces a drop in resolution to 848 × 480, produced the worst accuracy of all nine modes (2.76 mm), and 120 Hz at 1280 × 720 was significantly less accurate than 60 Hz at 1920 × 1080 in both air and water.
• Wide FOV degrades accuracy: At matched resolution and frame rate, narrow (90°) and medium (127°) fields of view did not differ significantly, whereas the wide FOV (170°) significantly increased reconstruction error.

In short, an action camera calibrated in water is a highly accurate measuring device, but the two settings most tempting for sports filming (maximum frame rate and widest field of view) are precisely the ones that degrade its metrological performance.

In subsequent work, the same group unified above- and underwater action cameras into a single bundle-adjusted volume measuring approximately 3 × 8 × 3.5 m (Bernardina et al., 2024; abstract only). Global mean absolute error remained below 1.5 mm, without degradation where trajectories crossed the air–water interface, and test-retest standard error stayed below 1 mm, enabling full 3D reconstruction of hand paths across five swimmers.

Motion blur: why exposure time matters more than frame rate

All of the calibration experiments reviewed above moved their reference bars and checkerboards slowly through the water. A swimmer’s hand moves at high speed, bringing into play two shutter-related errors that no spatial calibration can correct.

The first error is motion blur, which is determined by exposure duration (shutter speed) rather than frame rate. Following Payton, the systematic review recommends recording at 25 to 50 frames per second with a shutter speed between 1/350 and 1/750 s (Payton, as cited in Mooney et al., 2015). Underwater, image sharpness is degraded by both fluid turbulence and prolonged exposure times (Callaway et al., 2009). Because ambient light underwater is typically low, a camera left on automatic exposure lengthens its shutter time to maintain image brightness. Since proprietary auto-exposure algorithms are unpublished, the resulting blur cannot be predicted; consequently, shutter speed must be locked manually for quantitative filming (Pueo, 2016).

The spatial extent of motion blur ($\mathrm{\Delta }L$) is the product of object velocity ($v$) and exposure time ($\mathrm{\Delta }t$): $\mathrm{\Delta }L=v\cdot \mathrm{\Delta }t$. In sprint front crawl, 3D motion capture through pool windows shows that the hand reaches a mean velocity of 2.78 ± 0.36 m/s during the upsweep and 3.03 ± 0.28 m/s during the exit phase (Samson et al., 2015).

For a hand travelling at 3 m/s, the distance smeared across a single exposure is:

• 25 mm at 1/120 s;
• 12 mm at 1/250 s;
• 6 mm at 1/500 s;
• 3 mm at 1/1000 s.

Thus, even within the recommended range of 1/350 to 1/750 s, the fastest phase of the hand path exhibits several millimetres of motion blur, several times the roughly one-millimetre error of an in-water calibration.

Rolling shutter: why a frame is not a single instant

Shortening the exposure reduces blur, but does not guarantee geometric fidelity. While shutter speed governs how long each pixel is exposed, shutter architecture governs when different rows of pixels are exposed relative to one another:

1. Global shutter: Every pixel on the sensor is exposed simultaneously over the exact same time interval. Global shutters are standard in dedicated scientific high-speed cameras and represent the optimal architecture for motion analysis (Pueo, 2016).
2. Rolling shutter: The sensor exposes and reads out the frame sequentially row by row, from top to bottom. Virtually all cameras used by coaches and applied analysts (smartphones, action cameras, consumer camcorders) use rolling shutters. Consequently, a video frame is not an instantaneous snapshot, but a brief spatial-temporal scan; the interval between the first row and the last row is the readout time. A fast shutter speed freezes each individual row, but cannot prevent geometric skew when an object moves during the readout scan (Verhoeven, 2026).

Empirical readout times. Laboratory measurements establish the following readout durations for consumer devices:

• iPhone 3GS (video mode, 2010): approximately 30 ms from top row to bottom row (Forssén & Ringaby, 2010);
• GoPro HERO11 Black (photo mode): approximately 20 ms (Verhoeven, 2026; no published measurements for GoPro video mode were found);
• iPhone 17 Pro (video mode, 2026): between under 3 ms and 7.5 ms across its cameras and modes in trade-press laboratory testing (Machu, 2026).

Implications for swimming biomechanics. None of the swimming studies reviewed for this series reports camera shutter type or quantifies rolling-shutter distortion; papers report shutter speed only. We therefore derive our own kinematic estimate:

• Distortion of fast limb motion: While a 3 to 30 ms readout sweep runs from the top of the frame to the bottom, a hand moving at 3 m/s travels 1 to 9 cm. This represents the upper bound (for two landmarks positioned at opposite vertical edges of the sensor); landmarks close together vertically experience a proportionally smaller time lag. Nevertheless, a centimetre-scale skew vastly exceeds the 1–3 mm errors reported in calibration trials, whose reference bars and chessboards moved slowly (the chessboard at under 25 cm/s) and so could not reveal rolling-shutter artefacts (Silvatti et al., 2012b).
• Impact on competition race analysis: For race times and splits (resolved to 0.1 s), stroke rate, and mean segment velocity, a scan delay of a few milliseconds is negligible.
• Effect of camera orientation: Because readout proceeds vertically across the sensor rows, filming a horizontal swimmer from the side with the camera in landscape orientation confines the body to a narrow band of rows, the favourable case. Rotating the camera into portrait orientation directs the readout sweep along the swimmer’s longitudinal axis, maximising temporal skew between head and feet.
• Interaction with lighting flicker: Alternating-current luminaires pulse at twice the mains frequency (100 Hz on a 50 Hz grid, such as in Europe or New Zealand), which a rolling shutter converts into horizontal bands of varying brightness across the frame. High-grade LEDs exhibit 0–3 % flicker depth, whereas transformer-driven LEDs can flicker by 40–70 % (Pueo, 2016). While banding alters luminance rather than geometry, it can degrade contrast-based automated tracking (no published measurements of pool-lighting flicker were found).

Rigid stereo bars: do two cameras on one mount solve the problem?

Could researchers bypass repeated poolside calibrations by bolting two cameras to a single rigid bar? Here, a stereo pair denotes two cameras rigidly mounted on a common baseline bar, calibrated once as an integrated unit, and moved together. Its invariant relative geometry eliminates the need for on-site calibration, provided the waterproof housings are mechanically locked to the base bar, as any shift in separation or convergence angle introduces scale errors directly (Shortis, 2015).

In the swimming literature reviewed here, no study has employed a rigid stereo bar; 3D swimming studies mount two, four, six, or more cameras individually and calibrate them in situ (often applying the term “stereo pair” loosely to widely separated wall-mounted cameras). In marine science, by contrast, rigid stereo bars, often with two GoPros, are standard equipment for sizing fish underwater.

Lessons from marine stereo-video and geometric constraints:

1. Hardware protocol and fragility. In a standard marine field protocol, two housings are mounted 700 mm apart on a steel bar with a 7° inward convergence (or 500 mm apart at 5°; Langlois et al., 2020). Properly calibrated in water, such rigs achieve length errors of roughly 0.5 % in validation trials and 0.2–0.7 % on live fish (Shortis, 2015). Maintaining that calibration, however, requires strict operational discipline: electronic stabilisation must be disabled, field of view locked, and calibrations performed before and after every field campaign; even removing a camera from its housing to change a battery invalidates the calibration.
2. Quadratic error growth in depth. By stereo triangulation geometry, positional uncertainty across the image plane grows linearly with distance, whereas uncertainty along the line of sight (depth) grows with the square of the distance (Shortis & Harvey, 1998). A wider baseline counteracts depth degradation. In tests from 2 to 12 m (Boutros et al., 2015):
   • a 150 mm baseline lost precision at 6 m and degraded severely beyond 8 m;
   • a 400 mm baseline began to degrade at 9 m;
   • an 800 mm baseline maintained mean error near 0 % across all distances (in a separate comparison of calibration methods, a 3D calibration cube yielded 0.5 % mean error, compared with 1.7 % for an A3 checkerboard and 11.6 % for an A4 checkerboard).
3. Inadequacy of commercial depth cameras. Off-the-shelf stereo depth cameras feature narrow baselines (e.g., 75 mm on a Luxonis OAK-D; Luxonis, n.d.) and factory air calibrations that fail underwater, while active infrared depth projectors are absorbed by water within roughly 20 cm (Digumarti et al., 2016).
4. Geometrical estimate for a swimming pool. For a 1920-pixel frame width and a one-pixel disparity error at a working distance of 3 m from the swimmer, lateral error across the frame is roughly 2 mm. Along the line of sight (depth), however, a 75 mm baseline errs by ≈ 9 cm, whereas a 1 m stereo bar reduces depth error to ≈ 7 mm.

Net assessment for swimming:

• What a stereo bar solves: A rigid 1 m stereo bar yields true 3D coordinates for any landmark visible to both lenses, eliminating out-of-plane foreshortening of joint angles, and can be deployed without on-site frame or wand calibration at each session (provided the mount remains undisturbed and the two cameras are frame-synchronised via an in-view LED flash; Shortis, 2015).
• What it does not solve: Two cameras mounted side by side view the swimmer from nearly the same angle, leaving the far arm and leg occluded behind the torso. Any landmark obscured by bubbles in either lens is lost in 3D, and above-water recovery still requires a separate aerial system. Full-body 3D capture unavoidably requires wide camera spacing around the swimmer.

A practical protocol: camera settings for quantitative filming

What concrete settings should a coach or analyst lock in when filming to measure rather than merely to watch? The empirical findings above reduce to seven rules:

1. Calibrate in situ under identical optical settings. Calibrate in the water, through the exact same housing or viewing window, with the camera set exactly as it will record. Any subsequent change in zoom, lens mode (FOV), or resolution invalidates the calibration.
2. Align the calibration with the locus of motion. For 2D analysis, place the calibration scale strictly in the swimmer’s plane of motion (e.g., along the mid-lane centreline, never on the pool wall or lane rope). For 3D analysis, keep the swimmer inside the calibrated volume.
3. Disable electronic image stabilisation (EIS). Digital stabilisation shifts and warps individual frames to counter camera motion, altering the internal projection geometry from frame to frame; marine stereo protocols require it off (Langlois et al., 2020).
4. Prioritise narrow/medium FOV and spatial resolution over frame rate. Choose 1920 × 1080 at 60 fps in a narrow or medium field of view rather than 240 fps at 848 × 480 or a wide fisheye view.
5. Lock a fast shutter speed manually. Set exposure time by hand to match limb speed: for a hand moving at 3 m/s, 1/500 s limits blur to 6 mm, whereas 1/120 s produces a 25 mm smear.
6. Mount the camera stationary and in landscape orientation. Horizontal sensor alignment minimises the number of rolling-shutter scan rows spanned by the swimmer’s body.
7. Account for unavoidable occlusions. Turbulence and bubble trails obscure anatomical landmarks (Callaway et al., 2009), and no calibration can recover a point hidden from the lens.

Protocol in practice. Suppose a coach mounts a single housed action camera side-on at the pool wall to measure elbow angle during the pull. The protocol specifies: (a) stretching a calibration line down the middle of the lane in the swimmer’s plane and filming it through that housing; (b) turning stabilisation off; (c) selecting the narrow FOV at 1920 × 1080 and 60 fps; (d) locking shutter speed manually at 1/500 s or faster; and (e) mounting the camera in landscape. Even so, the setup remains 2D: only angles in the camera’s plane are measured at scale, and the far arm remains occluded. Measuring the hand’s transverse sweep beneath the torso requires 3D: multiple cameras calibrated together in the water.

Error propagation: why single millimetres matter

Why pursue millimetre-level accuracy when filming a human body? Because positional errors do not remain positional errors: angles computed between closely spaced landmarks amplify coordinate errors, and hydrodynamic force models amplify angular errors.

In the Vicon viewing-window study (Monnet et al., 2014), five miniature markers were attached to a swimmer’s hand to measure pitch and sweepback, the two orientation angles required by quasi-static hand-force models. Because one marker was occluded during the first half of the stroke, its coordinates had to be reconstructed from three neighbouring markers. Where true and reconstructed positions could be compared directly, the discrepancy was 5.6 ± 4.0 mm. Using that reconstructed marker shifted computed sweepback angles by 2.1 ± 1.6° and pitch angles by 1.4 ± 1.0°.

In an earlier study of the hand, inter-marker distances varied by 2.7 and 8.3 per cent during swimming, producing orientation errors of 10.1° in sweepback and 8.1° in pitch. When fed into quasi-static hydrodynamic equations, angular errors of that magnitude propagate into roughly a 27 per cent error in the lift coefficient and a 20 per cent error in the drag coefficient of the hand (Lauder et al., as cited in Monnet et al., 2014).

A coach comparing two freeze-frames on a screen does not need those millimetres; a biomechanical model converting digitised coordinates into propulsive hand forces does. Here the distinction established in Part 1 lands with full force: video measures kinematics, never kinetics, and inferring forces from kinematics requires models whose outputs are acutely sensitive to millimetre-level coordinate errors.

Summary of Part 2

1. Refraction and calibration models. Underwater measurement error stems primarily from refraction across the water–glass–air interface and how the calibration model accounts for it. Because refraction is systematic, calibrating directly in the water via wand bundle adjustment or a waterproof chessboard brings housed cameras (including consumer action cameras) down to roughly 1 mm of error. Conversely, applying a standard land calibration through pool windows multiplied a professional Vicon system’s error ninefold (to 5.75 mm), and linear DLT with a calibration frame leaves spatially dependent errors near 1 cm.
2. Shutter errors. Motion blur on a fast-moving hand (3 m/s) is cut to a few millimetres by setting a fast shutter speed manually (≤ 1/500 s), whereas rolling-shutter readout skew (3–30 ms) is not. Negligible for race analysis, rolling-shutter distortion can reach several centimetres on fast hand paths and remains unmeasured in the swimming literature.
3. Stereo-bar geometry. A rigid two-camera stereo bar eliminates repeated on-site calibrations, but suffers from quadratic depth-error growth at short baselines and cannot overcome self-occlusion of the far side of the body.
4. Error amplification. Millimetre precision is essential wherever video is used to estimate forces: a few millimetres of coordinate error on the hand amplify into degrees of orientation error and 20–27 % errors in estimated drag and lift coefficients.

Part 3 turns to the metric coaches ask about most frequently: swimming velocity.

The series

1. What a camera can measure
2. Water against optics: where the error budget lives (this article)
3. Velocity from video: from race splits to the stroke cycle
4. Starts and turns: hundredths of a second on camera
5. When the machine watches: markerless tracking and artificial intelligence

Parts 3 to 5 are being written; their titles are working ones.

References

1. Bernardina, G. R. D., Cerveri, P., Barros, R. M. L., Marins, J. C. B., & Silvatti, A. P. (2017). In-air versus underwater comparison of 3D reconstruction accuracy using action sport cameras. Journal of Biomechanics, 51, 77–82. https://doi.org/10.1016/j.jbiomech.2016.11.068
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