Abstract:
Fourier descriptors (FDs) provide an efficient and robust way of characterising object boundaries by integrating the versatile Fourier analysis into shape description. Despite their decades-long history and proven robustness in practical applications, the FDs are yet to be exploited to their full potential. There is, as yet, no concrete theory connecting the curve parameterisation to the number of FDs required for shape description. As there is an infinite number of parameterisation available, there must exist a parameterisation with the fewest number of FDs. A new method of computing FDs based on the t parameterisation is considered. The common way of computing FDs is simply applying the Fast Fourier Transform (FFT) to a set of complex coordinates representing the boundary of an object. The resulting FDs are parameterised by arc length. The new method uses t ∈ [0,1) as an alternative parameter and the curves are expressed by the complex Fourier series … By using linear programming techniques, the necessary algorithms for converting curves from the arc length parameterisation to the t parameterisation is implemented. Based on experimental results from both synthetic and real data, the t parameterisation is shown to be more efficient than the arc length parameterisation, as fewer FDs is needed for the sample curves. Given a set of few sample points, representing the boundary of an extremely small and pixelated object enclosing an area of few pixels, a method of realising a minimum energy simple closed curve through the samples is considered. The curve is also expressed in the form of complex Fourier series … The proposed method is implemented using linear programming techniques, but unfortunately, experimental results on synthetic data showed the algorithm is very inefficient. Therefore, the technique is considered a proof of concept and serves as a benchmark for future techniques.