A mathematical model based on an optimization formulation is presented for perceptual clustering of dot patterns. The features in the present model are its nonlinearity enabling the model to reveal hysteresis phenomena and its scale invariance. The clustering of dots is given by the mutual linking of dots by virtual lines. Every dot is assumed to be perceived at locations displaced from their original places. It is exemplified with simulations that the model can produce a hierarchical clustering of dots by variation in thresholds for the wiring of virtual lines and also the model can additionally reproduce some geometrical illusions semiquantitatively. This model is further extended for perceptual grouping in line segment patterns and geometrical illusions obsrved in those patterns are reproduced by the extended model.

A learning algorithm is presented for nearest neighbor pattern classifiers for the cases where mixed supervised and unsupervised training data are given. The classification rule includes rejection of outlier patterns and fuzzy classification. This partially supervised learning problem is formulated as a multiobjective program which reduces to purely super-vised case when all training data are supervised or to the other extreme of fully unsupervised one when all data are unsupervised. The learning, i. e. the solution process of this program is performed with a gradient method for searching a saddle point of the Lagrange function of the program.

A non-photorealistic rendering method creates oil-film-like images, expressed with colorful, smooth curves similar to the oil films generated on the surface of glass or water, from color photo images. The proposed method generates oil-film-like images through iterative processing between a bilateral infra-envelope filter and an unsharp mask. In order to verify the effectiveness of the proposed method, tests using a Lena image were performed, and visual assessment of oil-film-like images was conducted for changes in appearance as the parameter values of the proposed method were varied. As a result of tests, the optimal value of parameters was found for generating oil-film patterns.

Linear discriminant analysis (LDA) is one of the well-known schemes for feature extraction and dimensionality reduction of labeled data. Recently, two-dimensional LDA (2DLDA) for matrices such as images has been reformulated into symmetric 2DLDA (S2DLDA), which is solved by an iterative algorithm. In this paper, we propose a non-iterative S2DLDA and experimentally show that the proposed method achieves comparable classification accuracy with the conventional S2DLDA, while the proposed method is computationally more efficient than the conventional S2DLDA.

A function approximation scheme for image restoration is presented to resolve conflicting demands for smoothing within each object and differentiation between objects. Images are defined by probability distributions in the augmented functional space composed of image values and image planes. According to the fuzzy Hough transform, the probability distribution is assumed to take a robust form and its local maxima are extracted to yield restored images. This statistical scheme is implemented by a feedforward neural network composed of radial basis function neurons and a local winner-takes-all subnetwork.

A non-photorealistic rendering technique is presented for generating images such as stippling images and paper mosaic images with various shapes of paper pieces. Paper pieces are spatially arranged by using an anisotropic Lp poisson disk sampling. The shape of paper pieces is adaptively varied by changing the value of p. We demonstrate with experiments that edges and details in an input image are preserved by the pieces according to the anisotropy of their shape.

In this paper, we propose a method for selecting n-mode singular vectors in higher-order singular value decomposition. We select the minimum number of n-mode singular vectors, when the upper bound of a least-squares cost function is thresholded. The reduced n-ranks of all modes of a given tensor are determined automatically and the tensor is represented with the minimum number of dimensions. We apply the selection method to simultaneous low rank approximation of matrices. Experimental results show the effectiveness of the n-mode singular vector selection method.

An approach is described to synthesis and recognition of temporal patterns by using neural networks. A neural network is trained to produce prescribed waveforms with the steepest descent method which optimizes analog dynamics of neural networks described by differential equations. First a technique is developed for calculating error sensitivities with respect to network parameters by the adjoint network approach. Next an upper bound on timesteps is established to ensure the stability of the numerical solutions of the differential equations of networks. The effectiveness of these techniques are verified by several examples of learning of transient or oscillating waveforms with simple networks. In addition the complexity of the waveform is discussed which can be synthesized by a simple class of neural networks.

A modified deformable model is presented for constructing bijective topology preserving feature maps. The algorithm can solve the optimization problem in the input space as well as that in the output space. A saturating distance function alternative to the Euclid norm is employed to obtain compact space filling maps.

A simple and efficient semi-supervised classification method is presented. An unsupervised spectral mapping method is extended to a semi-supervised situation with multiplicative modulation of similarities between data. Our proposed algorithm is derived by linearization of this nonlinear semi-supervised mapping method. Experiments using the proposed method for some public benchmark data and color image data reveal that our method outperforms a supervised algorithm using the linear discriminant analysis and a previous semi-supervised classification method.

A method based on clustering is presented for restoring and segmenting gray scale images. An optimum clustering obtained by a gradient method gives an image with gray scale values which vary smoothly in each segmented region. The method is also applied to restoration from sparsely sampled data.

Fundamental nonlinear filters including M-filters and order statistic filters are formulated generally by the maximum a-posteriori (MAP) estimation and some filters are derived with the aid of the Bayes formula. This MAP-filters reduces to M-filters if a-priori probability distribution is uniform, while the rank filters are derived when a-priori bias exists in the MAP estimation. This MAP-filters are implemented with an analog electronic circuit and the log-likelihood is shown to be a Liapunov function for the dynamics of this circuit.

We propose a non-photorealistic rendering method for generating moire-picture-like color images from color photographs. The proposed method is performed in two steps. First, images with a staircasing effect are generated by a bilateral filter. Second, moire patterns are generated with an improved bilateral filter called an anti-bilateral filter. The characteristic of the anti-bilateral filter is to emphasize gradual boundaries.