Levenberg-Marquard Research Articles

Efficiency of non-linear lens distortion models in biomechanical analysis of human movement

Accurate camera calibration is required in applications, which involve quantitative measurements such as biomechanical analysis of the human movement. Some information concerning the measuring of human movement can be obtained by using uncalibrated cameras, however lens calibration is necessary when metric information is needed. When large field of view is required, wide-angle lenses are useful but they show significant non-linear distortion in the image. The aim of this study was to compare the accuracy of distortion models, which are used in biomechanical analysis of the human movement. A new calibration pattern was designed and the image of the calibration pattern was captured by using a wide-angle lens. The distorted image of the pattern was automatically processed to determine the dot centroids in the image. Lens distortion was modelled accounting for three sources of distortion: radial, decentring and thin prism distortions. These three effects result in seven distortion coefficients ( k 1, k 2, k 3, p 1, p 2, s 1, and s 2) in vertical and horizontal directions. Marzan and Karara (1975) [9] suggested 12, 14 and 16 parameters along with the Direct Linear Transformations (DLT) methods that comprise radial and decentring distortion models. In this study thin prism distortion [6] was also included to observe its effect. These non-linear distortion functions were minimised by using three different numerical methods, which were Least Squares, Levenberg–Marquard (LM) and Gauss–Newton (GM). In conclusion, the lens distortion models typically improved the accuracy. Applying the Non-linear Least Squares Optimisation Method (LM) showed the highest accuracy among the distortion models. While the average and the maximum error in the distorted image were 3.394% and 10.994%, respectively, they decreased to 1.591% and 3.524% in the application of DLT 18 method.

Classification of mitral stenosis from Doppler signals using short time Fourier transform and artificial neural networks

Doppler ultrasound is the most widely used diagnostic tool for assessing intracardiac blood flow. In this study diagnostic Doppler ultrasound signals were acquired from mitral valve of 125 patients referred to our institution and 55 healthy volunteers. Firstly the sonograms which represent the changes in Doppler frequency with respect to time were performed from mitral valve Doppler signals using short time Fourier transformation (STFT) method. Secondly the envelopes of these sonograms acquired and data set depicted from sonogram envelopes were applied to artificial neural networks (ANN) as input data. After the training phase, testing of the Levenberg Marquard (LM) backpropagation neural network was established. The overall results show that 97.8% correct classification was achieved, whereas 2 false classifications have been observed for the group of 92 people in test group. This result confirms that our technique contribute to the detection of mitral valve stenosis and our method offers more reliable information than looking at the sonogram on the Doppler screen and making a decision from the visual inspection.