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First published online March 28, 2008
Journal of Experimental Biology 211, 1305-1316 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.010272

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Automated visual tracking for studying the ontogeny of zebrafish swimming

Ebraheem Fontaine^1,*, David Lentink², Sander Kranenbarg², Ulrike K. Müller³, Johan L. van Leeuwen², Alan H. Barr⁴ and Joel W. Burdick¹

¹ Mechanical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
² Experimental Zoology Group, Wageningen University, Wageningen, The Netherlands
³ Department of Biology, California State University Fresno, Fresno, CA 93740, USA
⁴ Computer Science, California Institute of Technology, Pasadena, CA 91125, USA

View larger version (14K): [in this window] [in a new window]   Fig. 1. (A,B) Illustration of the modeling approach used for zebrafish. (A) Geometric mesh H(p) (green) with local tangent () and normal () vectors used to construct the mesh. The parameter and the function (u) define the position and shape of the model and are estimated during tracking. (B) Head region of length L is designated as rigid, while tail region bends according to linear combination of eight B-spline bases (u).

View larger version (10K): [in this window] [in a new window]   Fig. 2. Method for constructing fish model used in this analysis. The tangent vector associated with the function (u) is integrated to create the fish centerline. This centerline is combined with the fish's width profile R(u) to create the complete model H(p). R(u) remains fixed during tracking, and the bending of the model is modulated by changing the values of j, which control the shape of (u).

View larger version (5K): [in this window] [in a new window]   Fig. 3. Illustration of motion model of the fish. We assume that the total motion between frames k–l and k can be decomposed into undulatory motion and axial displacement. Note that figure displacements are exaggerated for illustration purposes. Actual motion between frames is much smaller due to the high frame rate of the camera.

View larger version (24K): [in this window] [in a new window]   Fig. 4. Measurement model for matching zebrafish images. (A) Initial estimate of the model location (white broken line) with matching edge feature points, ri (black filled, white circles). Red lines denote the 1D search regions for edge points. Note the tail is initially not matched to the boundary. (B) Final estimate of the model after four iterations. Although some error is present between the outline of the model and the actual fish, the centerline is accurately estimated based on visual inspection. Errors in the outline are due to small out of plane motions of the fish.

View larger version (20K): [in this window] [in a new window]   Fig. 5. At age 28 days, the fish has fully developed pectoral and caudal fins, which can cause incorrect model fitting if they are mistakenly classified as part of the boundary. To address this, we modify the juvenile fish model so that it does not take edge measurements in the pectoral and caudal regions.

View larger version (29K): [in this window] [in a new window]   Fig. 6. (A,B) Illustration of the initialization process used in the fish tracker. (A) The initial fish centerline (white), C(u), is estimated from the left (blue) and right (red) fish outlines. (B) This is used to estimate the width profile R(u) from the raw pixel data, BR and BL. Our modeling approach assumes a symmetric fish. Figure is zoomed into the head region because R(u) and pixel data are indistinguishable in the tail region.

View larger version (218K): [in this window] [in a new window]   Fig. 7. (A–F) Tracking results for zebrafish at (A,D) 5 d.p.f., (B,E) 15 d.p.f. and (C,F) 28 d.p.f. (see Movie 1 in supplementary material). The first row are wild type and the second row are stocksteif mutants. The raw centerlines estimated by the tracker are plotted at 1.3 ms intervals for 5 and 15 d.p.f. and 2.7 ms intervals for 28 d.p.f. Magenta and yellow trajectories indicate the paths of the tail and snout, respectively. Note in (C,F) that the caudal fin is not modeled in our current approach, so its motion is disregarded.

View larger version (10K): [in this window] [in a new window]   Fig. 8. Error estimates from tracking synthetic images generated with our model (A). This provides an upper bound on the accuracy that we can achieve with the current implementation. (B) Given noiseless images, we can localize the centerline of the fish to within 0.5% of its body length on average. Actual errors on real data will be slightly larger than this.

View larger version (25K): [in this window] [in a new window]   Fig. 9. Average error between the filtered and unfiltered data as a function of body axis position. The error for the centerline location (A,C) and curvature (B,D) are normalized to body length and measured at 51 uniformly spaced locations along the fish body. This provides an average deviation over time between the filtered and unfiltered data at particular locations along the fish. Small values are achieved for both wild-type and stocksteif fish, illustrating that our post-processing filtering technique retains most of the original information.

View larger version (136K): [in this window] [in a new window]   Fig. 10. (A–F) Specific curvature profiles for wild-type and mutant zebrafish at 5, 15 and 28 d.p.f. Black tick marks indicate the regions of approximate continuous swimming that are used in the frequency analysis of Fig. 12. Dotted white lines indicate approximate linear fit of zero curvature contour used to calculate wave speed.

View larger version (120K): [in this window] [in a new window]   Fig. 11. Angular acceleration of wild-type and stocksteif zebrafish at 5, 15 and 28 d.p.f. The largest accelerations are present near the tail tip where the body's moment of inertia is smallest. We observe the largest accelerations occurring during the initial tail beats when the fish is starting from rest. There is a significant difference in magnitude between the wild-type and stocksteif accelerations at 15 and 28 d.p.f.; however, similar values were achieved at 5 d.p.f.

View larger version (94K): [in this window] [in a new window]   Fig. 12. The magnitude of the curvature's Fourier transform during continuous swimming. The characteristic swimming frequency for each fish is calculated by taking a weighted average of the maximum frequency responses along the length of the fish. At 5 d.p.f., the fish have similar swimming frequencies. However, at 15 and 28 d.p.f., the stocksteif have slower swimming frequencies than the wild type. In addition, the 28 d.p.f. stocksteif primarily has undulations in the posterior 40% of its body due to its stiffer vertebrae.

View larger version (25K): [in this window] [in a new window]   Fig. 13. Displacement, speed and acceleration plots for the fish measured at the center of area (COA) of the dorsal view. Zero time indicates the onset of stimulus, and the MSE quintic spline method (Walker, 1998) is used to calculate speed and acceleration from the positions estimated by the model. Profiles measured at wild-type center of volume (COV) were determined using the method described by supplementary material Figs S1–S3.

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