FractalNet: A Neural Network Approach to Fractal Geometry
نویسنده
چکیده
This paper presents a multiply connected neural network designed to estimate the fractal dimension (Df) using the Box-counting method (BCM). Fractal analysis is a powerful shape recognition tool and has been applied to many pattern recognition problems. Additionally, the Box-Counting Method is one of the most popular methods for estimating Df. However, traditional methods used to estimate Df are sequential and have a computational cost of O(N log2(N)). A parallel method would be more efficient computationally and would suggest a possible biological realization. The architecture presented separates the calculation of Df into two sections, a data sampling section and a linear regression section. The data sampling section provides the ability to dyatically sample the data. The linear regression section simply calculates the slope of the best line through the sampling results. Finally, we show that the network scales well and can be designed to analyze 1-dimensional data or 2-dimensional data.
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تاریخ انتشار 2002