Abstract

Passive marker-based motion analysers are mainly used for studying human and animal movements. Biomedical applications are reported from different fields, e.g. (Jobbágy et al., 1998), (Muir et al, 1995), (Jobbágy et al., 1996).

The primary parameter provided by a video-based motion analyser is position. The parameters to be determined (e.g. torque, velocity, acceleration, jerk) require numerical differentiation. This operation means an extremely high noise amplification factor, thus the accuracy of position data is an important issue.

Many factors influence the resolution and accuracy of video based analysers: marker size (expressed in percentage of field of view, FOV), optical projection, lens distortion, parameters of the sensor (mostly CCD), the video/digital conversion, the calibration procedure (especially in case of 3D analysis) and the applied image processing algorithms.

Resolution and accuracy are not limited by the number of pixels on the sensor. When a marker image spreads over a number of pixels, then sub-pixel resolution and accuracy can be achieved by appropriate algorithms (Baca, 1996), (Jobbágy, 1994).

We tested a high performance, precision image based motion analyser, PRIMAS (Furnée, 1989). The measurement set-up and the evaluation method are suitable for general use in quantitative testing of marker based motion analysers. The paper also presents the resolution and accuracy analysis of a neurological application.

Keywords

motion analysis, accuracy, precision, resolution, sensor noise.
 

Measurements to characterise motion analysers

In the following we use the terms precision, resolution and accuracy for image-based motion analysers as defined in (Walton, 1986).

Precision analysis

Precision characterises the stability (reproducibility) of the system. High precision is necessary, but not satisfactory condition for accuracy.

Scenes with static markers were observed by the analyser under test (PRIMAS). Two types of measurement were made, (a) long-term measurement series started at power on with low sampling rate (1 hour recording time, 2 frames/s) and (b) short-term measurement series with high sampling rate (10 s recording time, 100 frames/s). The (a) type test reveals if thermal changes influence the position results while the (b) type test characterises system noise. During the experiments there was only one marker with 40 mm diameter in the FOV, which was 100 cm (horizontally) x 75 cm (vertically). The threshold level was set to the half of maximum intensity resulting in an average size extracted binary marker image spreading over 10 lines, consisting of cca. 120 pixels.

Figure 1 shows that the change within an hour in the measured horizontal position of the marker is approximately 0.9 pixel side. Taking into account the given set-up it is equal to 1.5 mm imaginary displacement meaning a 1/670 ratio of the horizontal side of FOV.

Short-term recordings are shown in Figure 2. The centre (x and y co-ordinates) of the same marker is measured 1000 times and the results are plotted against time (100 measurements were performed in each second).

The distribution of the measured centres along the sensor plane is shown in Figure 3.

It is clear that the distribution is not normal. It is difficult to characterise the precision of a device with a single value. The maximum deviation in the described experiment is 1/7500 (horizontally) and 1/7200 (vertically) compared to the appropriate side of the FOV. Precision depends on the marker image size, it increases if the marker image increases. Precision is closely related to noise.

The system noise was investigated by subtracting grey-scaled images taken from the same scene. An 8-bit A/D converter was built in the PRIMAS, which converted the intensity of a 64 x 16 pixel area of the CCD sensor. Figure 4 shows a typical subtracted image for the PRIMAS analyser. There were two markers in the field of view, though these cannot be located after subtraction. Let the intensity value of the (i, j)th pixel of the CCD sensor for two images be I₁(i, j) and I₂(i, j), 0 £ I £ 255, 1 £  i £  604, 1 £ j £ 288. The intensity value of this pixel after subtraction is D I₁₂(i, j) = I₁(i, j) - I₂(i, j). In the ideal case D I₁₂ would be zero for all pixels. The maximum values for D I₁₂ were found to be ± 5, independent of the scene and illumination. This noise results in different measured values for the centre of a static marker.

Resolution analysis

Resolution of a motion analyser is the smallest detectable displacement or the longest undetectable displacement.

Resolution of PRIMAS was measured with the help of a matrix printer (TECO VP2450). A marker was attached to the printing head that can be set into 775 equally spaced positions between the leftmost and the rightmost positions being 325 mm far from each other. The camera was 3.75 m far from the printer resulting in a 365 cm x 271 cm FOV. The distance between the neighbouring printing head positions was 0.419 mm. In case of horizontal marker movement, the minimal displacement was 1/8711 of the horizontal side of FOV.

The ping-pong ball size marker from this distance means a smaller than average marker image containing only 8-10 pixels. The printing head was moved into 10 consecutive positions from left to right and then back with the smallest possible displacement between neighbouring positions. The measured positions show a good correlation on the way there and back. This proves that the accuracy of the printing head settling is satisfactory. For all positions the measured values are different. This means that even for this small marker image the horizontal resolution of the device is better than 1/8700 of the FOV. Research work continues to find a measurement set-up for testing smaller marker image displacement. This could be reached by increasing the FOV but then the marker image would be unacceptably small. A larger FOV would require larger marker image and consequently larger marker. The other possibility is to assure smaller marker displacement. The usual FOV for the ping-pong ball sized markers is about 100 cm x 75 cm and the resolution estimated by simulation is in the order of 1/15000. A tool is required which is able to produce approximately 60 µ m displacement in at least 5 steps. This will be solved by the help of a micrometer.

Accuracy analysis

Testing of accuracy usually requires an etalon. When testing motion analysers the positions of the markers are generally not known with great enough accuracy. A widely used solution is to move a marker along a well defined trajectory, in the majority of cases a straight line. Accuracy is characterised on the basis of the deviations from the straight line. This test can be applied without knowing the exact marker positions.

The same set-up was used as for resolution analysis. The marker was moved horizontally with the help of the printing head and a straight line was fitted to the measured marker centre co-ordinates as shown in Figure 5. Figure 6 shows the distances between the measured values and the straight line. From these figures it is clear that the accuracy of the measurement is limited by the lens distortion. There are effective calibration procedures, which improve accuracy substantially.

 
Analysis of a biomedical application

A great number of diseases influence the movement patterns of patients. Neural diseases like Parkinson’s disease can be revealed in the early phase based on the analysis of hand- and finger movements. While evaluating the recorded position-time functions of the markers, physiological features like stiffness, rigidity, tremor, asymmetry are searched for applying signal processing algorithms. In a screening test the tested subjects must be classified based on the evaluation of the movement patterns. The analysis of the measurement set-up is necessary to select the appropriate signal processing algorithms. The set-up used for the tapping test is analysed in the following. This movement mimics piano playing. Both hands are on a table, initially all fingers touch the surface. Then all fingers except the thumbs are lifted, this is followed by hitting the surface again with the fingers in the following order: little, ring, middle and index. The tested subject is asked to perform this movement symmetrically with the two hands and as fast as he/she can. Figure 7 shows one hand of a person performing tapping test.

The signal processing algorithms and the result of a great number of healthy subjects and several Parkinsonian patients are described in (Jobbágy et al., 1998).

Markers are attached to the eight moving fingers with elastic ribbons. Marker size is limited, not to influence the movement. The markers we used had 10 mm diameters. The distance of the camera from the table is fixed, this assures the reproducibility and comparability of measurement results. Consequently the FOV must have been selected so that all fingers of a subject be seen during the movement. This requires that the horizontal size of the FOV be at least 50 cm, the actual value was 64 cm. Taking into account the ratio of horizontal and vertical sides of the FOV this means 48 cm for the vertical side. The sensor of the CCD camera has 604 columns and 288 rows, the 10 mm diameter marker results in a marker image covering an area on the sensor equivalent to 60 ... 80 pixels. This means sub-pixel resolution can be achieved. When binary images are generated (the video signal is thresholded to extract the marker image), the covered pixel co-ordinates can be averaged or the more accurate ring-fitting can be used (Jobbágy, 1994).

The noise limits resolution to 0.2 mm. The accuracy was measured by fixing the 10 mm diameter marker to the printing head and moving the head along a 30 cm line. The average distance between the fitted straight line and the measurement points was found to be 0.15 pixel side. For the diagonal of the FOV it means a 1/5000 accuracy. We repeated the measurement with smaller displacement, 5 cm. The accuracy in this case is approximately 1/4000 compared to the total length of the displacement. These parameters are sufficient for finger- hand- and arm movement measurements even without lens distortion compensation.

 
References