Sparse Array Image Correlation

Abstract

With the development of Holographic PIV (HPIV) and PIV Cinematography (PIVC), the need for a computationally efficient algorithm capable of processing images at video rates has emerged. This paper presents one such algorithm, sparse array image correlation. This algorithm is based on the sparse format of image data — a format well suited to the storage of highly segmented images. It utilizes an image compression scheme that retains pixel values in high intensity gradient areas eliminating low information background regions. The remaining pixels are stored in sparse format along with their relative locations encoded into 32 bit words. The result is a highly reduced image data set that retains the original correlation information of the image. Compression ratios of 30:1 using this method are typical. As a result, far fewer memory calls and data entry comparisons are required to accurately determine tracer particle movement. In addition, by utilizing an error correlation function, pixel comparisons are made through single integer calculations eliminating time consuming multiplication and Duport I., Benech floating point arithmetic. Thus, this algorithm typically results in much higher correlation speeds and lower memory requirements than spectral and image shifting correlation algorithms.

This paper describes the methodology of sparse array correlation as well as the speed, accuracy, and limitations of this unique algorithm. While the study presented here focuses on the process of correlating images stored in sparse format, the details of an image compression algorithm based on intensity gradient thresholding is presented and its effect on image correlation is discussed to elucidate the limitations and applicability of compression based PIV processing.