Erkki Oja

A new curve detection method: randomized Hough transform (RHT)

Abstract A new method is proposed for curve detection. For a curve with n parameters, instead of transforming one pixel into a hypersurface of the n -D parameter space as the HT and its variants do, we randomly pick n pixels and map them into one point in the parameter space. In comparison with the HT and its variants, our new method has the advantages of small storage, high speed, infinite parameter space and arbitrarily high resolution. The preliminary experiments have shown that the new method is quite effective.

Original Contribution: Principal components, minor components, and linear neural networks

Many neural network realizations have been recently proposed for the statistical technique of Principal Component Analysis (PCA). Explicit connections between numerical constrained adaptive algorithms and neural networks with constrained Hebbian learning rules are reviewed. The Stochastic Gradient Ascent (SGA) neural network is proposed and shown to be closely related to the Generalized Hebbian Algorithm (GHA). The SGA behaves better for extracting the less dominant eigenvectors. The SGA algorithm is further extended to the case of learning minor components. The symmetrical Subspace Network is known to give a rotated basis of the dominant eigenvector subspace, but usually not the true eigenvectors themselves. Two extensions are proposed: in the first one, each neuron has a scalar parameter which breaks the symmetry. True eigenvectors are obtained in a local and fully parallel learning rule. In the second one, the case of an arbitrary number of parallel neurons is considered, not necessarily less than the input vector dimension.

Modified Hebbian learning for curve and surface fitting

Abstract A linear neural unit with a modified anti-Hebbian learning rule is shown to be able to optimally fit curves, surfaces, and hypersurfaces by adaptively extracting the minor component (i.e., the counterpart of principal component) of the input data set. The learning rule is analyzed mathematically. The results of computer simulations are given to illustrate that this neural fitting method considerably outperform the commonly used least square fitting method in resisting both normal noise and outlier.

Self-organizing hierarchical feature maps

The topological feature map (TFM) algorithm introduced by T. Kohenen (1982) implements two important properties: a vector quantization (VQ) and a topology-preserving mapping. A tree-structured TFM (TSTFM) is presented as a computationally inexpensive alternative to the TFM algorithm. The computational complexity of the TSTFM is O (log N) rather than O(N) for the TFM. In addition, the TSTFM has some new properties that prove to be useful for VQ and in the context of visual perception: increased performance in VQ compared to the tree-structured VQ of A. Buzo et al. (1980) and hierarchical mapping of code vectors

Probabilistic and Non-Probabilistic Hough Transforms: Overview and Comparisons

Abstract A new and efficient version of the Hough transform for curve detection, the Randomized Hough Transform (RHT), has been recently suggested. The RHT selects n pixels from an edge image by random sampling to solve n parameters of a curve and then accumulates only one cell in a parameter space. In this paper, the RHT is related to other recent developments of the Hough transform. Hough transform methods are divided into two categories: probabilistic and non-probabilistic methods. An overview of these variants is given. Some novel extensions of the RHT are proposed to improve the RHT for complex and noisy images. These new versions of the RHT, called the Dynamic RHT, and the Window RHT with its variants, use local information of the edge image. They apply the RHT process to a limited neighbourhood of edge pixels. Tests in line detection with synthetic and real-world images demonstrate the high speed and low memory usage of the new extensions, as compared both to the basic RHT and other versions of the Hough transform.

Clustering Properties of Hierarchical Self-Organizing Maps

A multilayer hierarchical self-organizing map (HSOM) is discussed as an unsupervised clustering method. The HSOM is shown to form arbitrarily complex clusters, in analogy with multilayer feedforward networks. In addition, the HSOM provides a natural measure for the distance of a point from a cluster that weighs all the points belonging to the cluster appropriately. In experiments with both artificial and real data it is demonstrated that the multilayer SOM forms clusters that match better to the desired classes than do direct SOMs, classical k-means, or Isodata algorithms.

Randomized Hough transform (RHT)

A method is developed for calculating the Hough transform (HT) and completing the task of finding global features from binary edge images. The method is based on the fact that a single parameter space point can be determined uniquely with a pair, triple, or generally n-tuple of points from the original picture. Such n-tuples of points can be chosen randomly from the edge image, giving the method the name randomized Hough transform (RHT). The new algorithm reduces the computation time and memory use of the HT drastically. In the standard HT one must calculate one parameter curve in the parameter space for one pixel, whereas in the RHT only one parameter point has to be solved for one n-tuple of points, and the presence of a specific curve in the image is quickly revealed by the accumulation of a small number of parameter points.<<ETX>>

Detecting texture periodicity from the co-occurrence matrix

Abstract Cooccurrence histograms have been widely used in texture and signal analysis. There have been suggestions on how to find structure and periodicity of the texture from cooccurrence histograms. A statistical property called agreement is here recommended as an indication of periodic structure. It is measured by a κ statistic.

Comparisons of Probabilistic and Non-probabilistic Hough Transforms

A new and efficient version of the Hough Transform for curve detection, the Randomized Hough Transform (RHT), has been recently suggested. The RHT selects n pixels from an edge image by random sampling to solve n parameters of a curve and then accumulates only one cell in a parameter space. In this paper, the RHT is related to other recent developments of the Hough Transform by experimental tests in line detection. Hough Transform methods are divided into two categories: probabilistic and non-probablistic methods. Four novel extensions of the RHT are proposed to improve the RHT for complex and noisy images. These apply the RHT process to a limited neighborhood of edge pixels. Tests with synthetic and real-world images demonstrate the high speed and low memory usage of the new extensions, as compared both to the basic RHT and other versions of the Hough Transform.

Improved Simulated Annealing, Boltzmann Machine, and Attributed Graph Matching

By separating the search control and the solution updating of the commonly used simulated annealing technique, we propose a revised version of the simulated annealing method which produces better solutions and can reduce the computation time. We also use it to improve the performance of the Boltzmann machine. Furthermore, we present a simple combinatorial optimization model for solving the attributed graph matching problem of e.g. computer vision and give two algorithms to solve the model, one using our improved simulated annealing method directly, the other using it via the Boltzmann machine. Computer simulations have been conducted on the model using both the revised and the original simulated annealing and the Boltzmann machine. The advantages of our revised methods are shown by the results.