Recursive Gaussian derivative filters

Abstract

We propose a new strategy to design recursive implementations of the Gaussian filter and Gaussian regularized derivative filters. Each recursive filter consists of a cascade of two stable N th -order subsystems (causal and anti-causal). The computational complexity is 2N multiplications per pixel per dimension independent of the size (σ) of the Gaussian kernel. The filter coefficients have a closed-form solution as a function of scale (σ) and recursion order N (N=3,4,5). The recursive filters yield a high accuracy and excellent isotropy in n-D space.

Motion-Driven Segmentation by Competitive Neural Processing

“…Similar approaches have been implemented using this technology to achieve realtime processing [33,34]. The hardware resources required for the motion layer can be reduced by implementing the Gaussian derivatives with recursive filters available in the literature [35], which reduce the external memory requirements. The parallelism of FPGA technology allows functional unit replication which can be used to implement multiple neuron processing in parallel.…”

Local Jet Based Similarity for NL-Means Filtering

“…To keep this acceleration significant however, efficient methods must be used to compute the local jet. We use the recursive implementation of the Gaussian and its derivatives proposed in [13], which allows to compute the 6 components of the local jet in constant time per pixel, for any σ.…”

Learning spatial relations in object recognition

“…In practice, to acquire great computational advantages, we approximate the Gaussian derivatives, similar to recursive implementation [103,33], by B-spline [101,102], see figure 5.4. A B-spline of order n denoted by β n (z) is generated by convolving n + 1 times β 0 (z) with itself The nth order derivative of the B-spline can be obtained from the (n − 1)th order B-spline as follows…”