Figure 1.
EOD signal measurement and ideal dipole approximation.
A) Our experimental setup. Electrodes were attached on the tank wall, and concurrent video recordings were made under infrared illumination. B) Received signal intensity (RSI) measurement. The original waveforms (green) were rectified then summed from all channels (blue). Signal envelope (red curve) was extracted using an RMS filter, and a pulse timing reference (thick grey) was determined at the peak. An instantaneous slope of the original waveform was measured at 250 µsec before the reference timing (red line). C) Ideal dipole voltage (Vdip) approximation of an electric fish in two dimensions. D) Lookup table search using a dot-product to find the best matching vector.
Figure 2.
Experimental data fitted by the ideal dipole model.
A) The measured RSI values (slopes of differential voltages) closely agree (ρcorr = 0.9983) with the RSI predicted by the ideal dipole model. B) The error distribution of the RSI values normalized to the SD of the measurement averaged across the whole tank. The errors were computed by the measured values minus the predicted values. C) The RSI error plotted as a function of the distance from the tank wall. The distance was measured to the center of the body. The edges of the boxes represent 25th and 75th percentiles, and the center mark (red line) is the median. Outliers are individually plotted in red. D) The normalized RSI error as a function of the normalized measured RSI. The RSI values were each grouped within the range of ±0.25.
Figure 3.
Comparison of the simulated noise performances of the four electrode configurations.
A) The four types of electrode configurations tested in simulations. Filled circles represent positive electrodes and open circles represent negative electrodes for the differential voltage measurements. Electrodes pairs are connected with lines. B) The position errors plotted as a function of the simulated noise intensity (plotted on a log-log scale). The noise intensities were normalized to the SD of the measurement. C) The orientation errors plotted as a function of the simulated noise intensity (plotted on a log-log scales).
Table 1.
Comparison of the LUT search methods.
Figure 4.
Optimization of the dipole search algorithm.
A) The circular tank is partitioned by the LUT indices, which are determined by the absolute maximum channels at each dipole location. In this illustration, the orientation of the dipole ( = θdip) was set equal to its angular position ( = θpos). The electrodes are shown as black (positive) or white (negative) circles, and their fill colors correspond to their channel indices. The channel numbers 1 to 8 correspond to the colors from blue to red as indicated. B) Cumulative improvements in the search speed after successively applying the optimization techniques (original: single search step, single: single numerical precision, indexed: LUT indexed by the strongest channel, two-step: two-step search procedure, cached: fine-grid search was cached with nhistory = 16).
Figure 5.
Single fish tracking accuracy.
A) The error distribution of the dipole tracking for the four (blue) and eight (red) channel configurations (Obs. Prob.: Observation probability). B) The tracking accuracy improved after excluding the channel nearest to the fish within a set exclusion distance. C) The tracking errors were plotted vs. the distance from the tank wall. On each box, the central mark (red line) is the median, the edges of the box are the 25th and 75th percentiles, and the whiskers extend to the most extreme data points not considered outliers. Outliers are plotted individually (red markers): a value that is more than 1.5 times the interquartile range away from the top or bottom of the box as determined using the boxplot function (Statistics toolbox for Matlab). D) The error distributions of the dipole tracking near (<10 cm, red) and far (>10 cm, blue) from the tank wall.
Table 2.
Summary of the tracking accuracy under different test conditions.
Figure 6.
Effects of an object on the dipole tracking accuracy.
A) The three object locations tested are marked in red circles, and our coordinates system is shown. B) The dipole tracking errors for the three object locations and the control (no obj.: no object placed) averaged over all locations visited by fish for 666.7 sec. C) A false color representation of the dipole tracking errors when fish passes by an object. The visually determined traces are shown in grey, and the object is marked as a red circle. D) The error distributions of the dipole tracking near (<20 cm, red) and far (>20 cm, blue) from the object’s surface.
Figure 7.
Effects of tail bending on the dipole tracking accuracy.
A) Tail-bending angles were visually determined (left) using three feature points (head, tail, and center of the body), and also electrically determined using two dipoles at the central and one in the tail regions (right). B) The electrically determined tail-bending angles correlated well (ρcorr = 0.7631) with the visually determined values. C) The dipole tracking errors plotted as a function of the tail-bending angles. D) The error distributions of the dipole tracking for the small (<10°) and large (>10°) tail-bending angles. The locations near the tank wall (<10 cm) were excluded from our analysis to remove the near-field effect.
Figure 8.
A) The traces of two fish were separated after the dipole localization. B) Comparison of the tracking errors between the single and dyads tracking for each fish. C) A false color representation of the tracking errors during close encounter between animals. Fish images were superimposed every 1 sec interval, and the larger fish is shown darker (Fish #1). D) The error distributions of the dipole tracking at a close (<40 cm) and far (>40 cm) distance between fish. The distances were measured to the center of the body, and the locations near the tank wall (<10 cm) were excluded from our analysis to remove the near-field effect.