We propose a fast agglomerative clustering method using an approximate nearest neighbor graph for reducing the number of distance calculations. The time complexity of the algorithm is improved from O(tauN2) to O(tauNlogN) at the cost of a slight increase in distortion; here, tau denotes the number of nearest neighbor updates required at each iteration. According to the experiments, a relatively small neighborhood size is sufficient to maintain the quality close to that of the full search.
The pairwise nearest neighbor (PNN) method is a simple and well-known method for codebook generation in vector quantization. In its exact form, it provides a good-quality codebook but at the cost of high run time. A fast exact algorithm was recently introduced to implement the PNN an order of magnitude faster than the original O(N 3 K) time algorithm. The run time, however, is still lower bounded by O(N 2 K), and therefore, additional speed-ups may be required in applications where time is an important factor. We consider two practical methods to reduce the amount of work caused by the distance calculations. Through experiments, we show that the run time can be reduced to 10 to 15% that of the original method for data sets in color quantization and in spatial vector quantization.
We propose a fast pairwise nearest neighbor (PNN)based O(N log N) time algorithm for multilevel nonparametric thresholding, where N denotes the size of the image histogram. The proposed PNN-based multilevel thresholding algorithm is considerably faster than optimal thresholding. On a set of 8 to 16 bits-per-pixel real images, experimental results also reveal that the proposed method provides better quality than the Lloyd-Max quantizer alone. Since the time complexity of the proposed thresholding algorithm is log linear, it is applicable in real-time image processing applications.
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