ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3.3 Identification of Paths
According to the results shown in Figure 1c, and using the features of the library cvblobslib
are captured initial positions of each sperm, then through a 7x7 observation window is tracked
to each, calculating the next coordinate by the proximity in the area covering the window
generated by storing the coordinates obtained in each frame. Figure 1d shows the result.
3.4 Kalman filter
In some cases sperm cells cross each other, this can lead to a loss or confusion of the path. To
avoid this, using a Kalman filter for each spermatozoa which is executed only at the time
identified two or more sperm in a same observation window. The Kalman filter consists of 2
phases (7). In the prediction phase, generate a prediction of the future state in time, taking into
account all available information at that time. In the correction phase, it is estimated an
improved prediction of the state, so the error is minimized statistically.
3.4.1 Prediction Phase.
Position data and velocity are obtained as explained in section 3.3 and stored in the vector
paths, only to be recorded in the state vector, shown in equation (1). After determining the
error covariance matrix called matrix , which represents learning for error correction using
equation (2).
(1)
(2)
3.4.2 Phase Correction
In this phase, the update time in the state estimation for the prediction is corrected in the error
covariance matrix P and the Kalman Filter difference is calculated to minimize the error in
estimating the new state. The gain of the filter and the updated values and described in
equations (3), (4) and (5).
3.5 Features Extraction
The objective classification of sperm cells trajectories is performed using the following
descriptors. Curvilinear Velocity (VCL), Average Path Velocity (VAP), Straight Line
Velocity (VSL), Linearity (LIN), Wobble (WOB), Progression (PROG), Beat cross frequency
(BCF), Crossover Approximations Frequency (CAF), Movement Statistic Mode (MSM), a
sample of these values are shown in Table. 1. Figure 2a shows a detailed description of the
types of paths.
3.5.1 VCL
Is the point to point displacement average velocity of the sperm cell, divided by the duration
of the video, as shown in equation (6).
(3)
(4)
(5)