A Mathematical Model for Transformation Matrices in Ultrasound Probe Positioning and Orientation

This paper produces a novel approach to determine the position and orientation of an ultrasound probe in 3D space. The probe carries an orthogonal set of laser lines that project onto two orthogonal planes, and a pair of high-resolution Pi cameras are positioned orthogonal to each other while facing the two planes to capture the laser lines appearing on these planes. This approach is unlike traditional methods that guide the placement of a probe based on operator skill. Basic functions of the system work with image processing algorithms, so the endpoint of the two laser lines are found on the processed images and thus the transformation matrix that describes probe position and orientation is calculated in the predefined coordinate system. Parameters of translation and rotation are derived from this matrix, where multiple iterations of the transformation are performed in real time to minimize the error. Using this methodology brings in a strong solution for positioning the probe more precisely in a 3D space, which is a huge step forward compared to traditional methods which lack computational support. The results demonstrate the ability of this method to accurately determine the initial position and orientation of the probe. Echocardiogram imaging systems guided by artificial intelligence depend on very accurate probe position and orientation information to improve their capacity to offer real-time, patient-specific recommendations on the probe position giving out the highest quality images.