Extraction and Reduction of the Parameters of Archimedes Spirals Drawn by Patients

Abstract Analysis of patient’s hand drawn Archimedes spirals is commonly used in the medical community to grade various forms of tremors. These spirals are often drawn on paper using a pen or a pencil and then Xeroxed/scanned to turn the drawings into computer images. This process introduces artifacts such as misalignment of the paper, finite/variable width of the drawn line, light grey marks left by the toner, and greyscale background pixels introduced by the Xeroxing/scanning steps. Even a spiral drawn directly on the screen of a tablet produces lines with multi-pixel widths and varying greyscale values. These artifacts make it difficult to use image processing techniques to automatically extract the patient’s spiral as a clean single-valued discrete signal which could be treated mathematically for further analysis. We present a procedure in this paper to extract the patient’s hand-drawn spiral automatically as a mathematical discrete signal even in the presence of artifacts, with minimal user intervention. We also note that the spirals used by some hospitals and clinics are distorted and not perfect Archimedes spirals; nevertheless, our procedure can still be used for these cases. The extracted discrete signal is composed of a couple of thousand samples (features). The largeness of this feature space compared with the typical number of spiral samples at our disposal (of the order of only hundreds) makes it infeasible to apply Machine Learning techniques for predictions which generalize well in the real world without overfitting. We analyze the extracted discrete signal using FFT (Fast Fourier Transforms) and show that in FFT space the signal can be represented by as few as 300 parameters. The paper concludes that if these 300 parameters (or even 150 parameters for some problems) are used as a feature set for Machine Learning then it could very well be possible to make predictions which generalize well to the real world without overfitting. As a note, applications to actual Machine Learning problems are not covered in this paper.