In this paper, a new robust model fitting method is proposed to efficiently segment multistructure data even when they are heavily contaminated by outliers. The proposed method is composed of three steps: first, a conventional greedy search strategy is employed to generate (initial) model hypotheses based on the sequential "fit-and-remove" procedure because of its computational efficiency. Second, to efficiently generate accurate model hypotheses close to the true models, a novel global greedy search strategy initially samples from the inliers of the obtained model hypotheses and samples subsequent data subsets from the whole input data. Third, mutual information theory is applied to fuse the model hypotheses of the same model instance. The conventional greedy search strategy is used to generate model hypotheses for the remaining model instances, if the number of retained model hypotheses is less than that of the true model instances after fusion. The second and the third steps are performed iteratively until an adequate solution is obtained. Experimental results demonstrate the effectiveness and efficiency of the proposed method for model fitting.

This paper approaches the problem of geometric multi-model fitting as a data segmentation problem. The proposed solution is based on a sequence of sampling hyperedges from a hypergraph, model selection and hypergraph clustering steps. We developed a sampling method that significantly facilitates solving the segmentation problem using a new form of the Markov-Chain-Monte-Carlo (MCMC) method to effectively sample from hyperedge distribution. To sample from this distribution effectively, our proposed Markov Chain includes new ways of long and short jumps to perform exploration and exploitation of all structures. To enhance the quality of samples, a greedy algorithm is used to exploit nearby structure based on the minimization of the Least k th Order Statistics cost function . Unlike common sampling methods, ours does not require any specific prior knowledge about the distribution of models. The output set of samples leads to a clustering solution by which the final model parameters for each segment are obtained. The method competes favorably with the state-of-the-art both in terms of computation power and segmentation accuracy.

Identifying the underlying models in a set of data points that is contaminated by noise and outliers leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher-order affinities between data points into a graph, which can be clustered using spectral clustering. Calculating all possible higher-order affinities is computationally expensive. Hence, in most cases, only a subset is used. In this paper, we propose an effective sampling method for obtaining a highly accurate approximation of the full graph, which is required to solve multi-structural model fitting problems in computer vision. The proposed method is based on the observation that the usefulness of a graph for segmentation improves as the distribution of the hypotheses that are used to build the graph approaches the distribution of the actual parameters for the given data. In this paper, we approximate this actual parameter distribution by using a th-order statistics-based cost function, and the samples are generated using a greedy algorithm that is coupled with a data sub-sampling strategy. The experimental analysis shows that the proposed method is both accurate and computationally efficient compared with the state-of-the-art robust multi-model fitting techniques. The implementation of the method is publicly available from https://github.com/RuwanT/model-fitting-cbs.

The extension of conventional clustering to hypergraph clustering, which involves higher order similarities instead of pairwise similarities, is increasingly gaining attention in computer vision. This is due to the fact that many clustering problems require an affinity measure that must involve a subset of data of size more than two. In the context of hypergraph clustering, the calculation of such higher order similarities on data subsets gives rise to hyperedges. Almost all previous work on hypergraph clustering in computer vision, however, has considered the smallest possible hyperedge size, due to a lack of study into the potential benefits of large hyperedges and effective algorithms to generate them. In this paper, we show that large hyperedges are better from both a theoretical and an empirical standpoint. We then propose a novel guided sampling strategy for large hyperedges, based on the concept of random cluster models. Our method can generate large pure hyperedges that significantly improve grouping accuracy without exponential increases in sampling costs. We demonstrate the efficacy of our technique on various higher-order grouping problems. In particular, we show that our approach improves the accuracy and efficiency of motion segmentation from dense, long-term, trajectories.

In this paper we propose a novel algorithm for PAPR reduction of an OFDM system, based on a companding scheme. In this method a compressing polynomial is appended to the IFFT block at the transmitter and at the receiver the FFT block is combined with a reverse expanding function where the iterative Jacobi's method is used for solving equations. The proposed method entails less complexity at the transmitter in comparison with other PAPR reduction algorithms. It also requires less increase in SNR for the same BER compared to other companding methods. A trade off between complexity and performance can set the order of compressing polynomial and the number of iterations for the proposed algorithm at the receiver