Efficient Computation of Convolution of Huge Images

Abstract

Abstract. In image processing, convolution is a frequently used operation. It is an important tool for performing basic image enhancement as well as sophisticated analysis. Naturally, due to its necessity and still continually increasing size of processed image data there is a great demand for its efficient implementation. The fact is that the slowest algorithms (that cannot be practically used) implementing the convolution are capable of handling the data of arbitrary dimension and size. On the other hand, the fastest algorithms have huge memory requirements and hence impose image size limits. Regarding the convolution of huge images, which might be the subtask of some more sophisticated algorithm, fast and correct solution is essential. In this paper, we propose a fast algorithm implementing exact computation of the shift invariant convolution over huge multi-dimensional image data.

Versatile algorithms for the computation of 2-point spatial correlations in quantifying material structure

“…We address the challenge described above using a strategy that carefully partitions the large domain into smaller subdomains, performs the requisite computations on them, and then assembles correctly the statistics for the original large domain from the computations on the subdomains. Our approach can be compared to various partitioning strategies for efficient computation of convolutions via FFTs that are well known in digital signal processing applications, such as overlap-save, overlap-add, and hybrid schemes [64,65]. The overall process is illustrated schematically for a 2-D dataset in Fig.…”

Algorithms for Efficient Computation of Convolution

“…Although the concept of the fast Fourier transform [54] and the frequency-based convolution [55] is several decades old, with new architectures upcoming, one has to deal with new problems. For example, the efficient access to the memory was an important issue in 1970s [56] just as it is today [21,23]. Another problem to be considered is the numerical precision [57].…”

“…This means that the input signal and kernel will be split into smaller pieces, so called tiles that need not be of the same size. Hence, we will try to reduce the memory requirements while keeping the efficiency of the whole convolution process as proposed in [23]. 2 The size of padded signal should be exactly (N f + N g − 1).…”

“…• Data can be split in time domain according to overlap-save and overlap-add scheme [22,23], respectively. Combining these two schemes with fast convolution one can receive a quasi-optimal solution that can be efficiently computed on any computer.…”

Towards a Realistic Distribution of Cells in Synthetically Generated 3D Cell Populations

“…The improvement is, nevertheless, at the expense of increased memory demand. The memory demand can be, however, considerably reduced if the technique designed in [11] is used.…”