We present an alternative approach to what we call the "standard optimization", which minimizes a cost function by searching a parameter space. Instead, our approach "projects" in the joint observation space onto the manifold defined by the "consistency constraint", which demands that any minimal subset of observations produce the same result. This approach avoids many difficulties encountered in the standard optimization. As typical examples, we apply it to line fitting and multiview triangulation. The latter produces a new algorithm far more efficient than existing methods. We also discuss the optimality of our approach.

The spatio-temporal multiple view geometry can represent the geometry of multiple images in the case where non-rigid arbitrary motions are viewed from multiple translational cameras. However, it requires many corresponding points and is sensitive to the image noise. In this paper, we investigate mutual projections of cameras in four-dimensional space and show that it enables us to reduce the number of corresponding points required for computing the spatio-temporal multiple view geometry. Surprisingly, take three views for instance, we no longer need any corresponding point to calculate the spatio-temporal multiple view geometry, if all the cameras are projected to the other cameras mutually for two time intervals. We also show that the stability of the computation of spatio-temporal multiple view geometry is drastically improved by considering the mutual projections of cameras.

We propose a character size optimization technique to reduce the number of EB shots of multi-column-cell (MCC) lithographic systems in which transistor patterns are projected with multiple column cells in parallel. Each and every column cell is capable of projecting patterns with character projection (CP) and variable shaped beam (VSB) methods. Seeking the optimal character size of characters contributes to minimizing the number of EB shots and reducing the fabrication cost for ICs. Experimental results show that the character size optimization achieved 70.6% less EB shots in the best case with an available electron beam (EB) size. Our technique also achieved 40.6% less EB shots in the best case than a conventional character sizing technique.

In this paper, we propose a novel target acoustic signal detection approach which is based on non-negative matrix factorization (NMF). Target basis vectors are trained from the target signal database through NMF, and input vectors are projected onto the subspace spanned by these target basis vectors. By analyzing the distribution of time-varying normalized projection error, the optimal threshold can be calculated to detect the target signal intervals during the entire input signal. Experimental results show that the proposed algorithm can detect the target signal successfully under various signal environments.

We propose the multi-domain adaptive learning that enables us to find a point meeting possibly time-varying specifications simultaneously in multiple domains, e.g. space, time, frequency, etc. The novel concept is based on the idea of feasibility splitting -- dealing with feasibility in each individual domain. We show that the adaptive projected subgradient method (Yamada, 2003) realizes the multi-domain adaptive learning by employing (i) a projected gradient operator with respect to a ‘fixed’ proximity function reflecting the time-invariant specifications and (ii) a subgradient projection with respect to ‘time-varying’ objective functions reflecting the time-varying specifications. The resulting algorithm is suitable for real-time implementation, because it requires no more than metric projections onto closed convex sets each of which accommodates the specification in each domain. A convergence analysis and numerical examples are presented.

Teeth segmentation in computed tomography (CT) images is a major and challenging task for various computer assisted procedures. In this paper, we introduced a hybrid method for quantification of teeth in CT volumetric dataset inspired by our previous experiences and anatomical knowledge of teeth and jaws. In this regard, we propose a novel segmentation technique using an adaptive thresholding, morphological operations, panoramic re-sampling and variational level set algorithm. The proposed method consists of several steps as follows: first, we determine the operation region in CT slices. Second, the bony tissues are separated from other tissues by utilizing an adaptive thresholding technique based on the 3D pulses coupled neural networks (PCNN). Third, teeth tissue is classified from other bony tissues by employing panorex lines and anatomical knowledge of teeth in the jaws. In this case, the panorex lines are estimated using Otsu thresholding and mathematical morphology operators. Then, the proposed method is followed by calculating the orthogonal lines corresponding to panorex lines and panoramic re-sampling of the dataset. Separation of upper and lower jaws and initial segmentation of teeth are performed by employing the integral projections of the panoramic dataset. Based the above mentioned procedures an initial mask for each tooth is obtained. Finally, we utilize the initial mask of teeth and apply a variational level set to refine initial teeth boundaries to final contour. In the last step a surface rendering algorithm known as marching cubes (MC) is applied to volumetric visualization. The proposed algorithm was evaluated in the presence of 30 cases. Segmented images were compared with manually outlined contours. We compared the performance of segmentation method using ROC analysis of the thresholding, watershed and our previous works. The proposed method performed best. Also, our algorithm has the advantage of high speed compared to our previous works.

To attain good performance in an acoustic echo cancellation system, it is important to have a variable step size (VSS) algorithm as part of an adaptive filter. In this paper, we are concerned with the development of a VSS algorithm for a recently proposed subband affine projection (SAP) adaptive filter. Two popular VSS algorithms in the literature are the methods of delayed coefficients (DC) and variable regularization (VR). However, the merits and demerits of them are mutually exclusive. We propose a VSS algorithm that is a hybrid of both methods and combines their advantages. An extensive study of the new algorithm in different scenarios like the presence double-talk (DT) during the transient phase of the adaptive filter, DT during steady state, and varying DT power is conducted and reasoning is given to support the observed behavior. The importance of the method of VR as part of a VSS algorithm is emphasized.

The block based motion estimation technique is adopted by various video coding standards to reduce the temporal redundancy in video sequences. The core of that technique is the search algorithm implemented to find the location of the best matched block. Indeed, the full search algorithm is the most straightforward and optimal but computationally demanding search algorithm. Consequently, many fast and suboptimal search algorithms have been proposed. Reduction of the number of location being searched is the approach used to decrease the computational load of full search. In this paper, hybridization between an adaptive search algorithm and the full search algorithm is proposed. The adaptive search algorithm benefits from the correlation within spatial and temporal adjacent blocks. At the same time, a feature domain based matching criteria is used to reduce the complexity resulting from applying the pixel based conventional criteria. It is shown that the proposed algorithm produces good quality performance and requires less computational time compared with popular block matching algorithms.

In this paper, we propose designing method for separable-denominator two-dimensional Infinite Impulse Response (IIR) filters (separable 2D IIR filters) by Successive Projection (SP) methods using the stability criteria based on the system matrix. It is generally known that separable 2D IIR filters are stable if and only if each of the denominators is stable. Therefore, the stability criteria of 1D IIR filters can be used for separable 2D IIR filters. The stability criteria based on the system matrix are a necessary and sufficient condition to guarantee stability in 1D IIR filters. Therefore, separable 2D IIR filters obtained by the proposed design method have a smaller error ripple than those obtained by the conventional design method using the stability criterion of Rouche's theorem.

Character projection (CP) lithography is utilized for maskless lithography and is a potential for the future photomask manufacture because it can project ICs much faster than point beam projection or variable-shaped beam (VSB) projection. In this paper, we first present a projection mask set development methodology for multi-column-cell (MCC) systems, in which column-cells can project patterns in parallel with the CP and VSB lithographies. Next, we present an INLP (integer nonlinear programming) model as well as an ILP (integer linear programming) model for optimizing a CP mask set of an MCC projection system so that projection time is reduced. The experimental results show that our optimization has achieved 33.4% less projection time in the best case than a naive CP mask development approach. The experimental results indicate that our CP mask set optimization method has virtually increased cell pattern objects on CP masks and has decreased VSB projection so that it has achieved higher projection throughput than just parallelizing two column-cells with conventional CP masks.

This paper proposes a novel algorithm for image feature extraction-the dual two-dimensional fuzzy class preserving projections ((2D)2FCPP). The main advantages of (2D)2FCPP over two-dimensional locality preserving projections (2DLPP) are: (1) utilizing the fuzzy assignation mechanisms to construct the weight matrix, which can improve the classification results; (2) incorporating 2DLPP and alternative 2DLPP to get a more efficient dimensionality reduction method-(2D)2LPP.

Recently, a data-selective method has been proposed to achieve low misalignment in affine projection algorithm (APA) by keeping the condition number of an input data matrix small. We present an improved method, and a complexity reduction algorithm for the APA with the data-selective method. Experimental results show that the proposed algorithm has lower misalignment and a lower condition number for an input data matrix than both the conventional APA and the APA with the previous data-selective method.

This letter presents a new mathematical expression for the excess mean-square error (EMSE) of the affine projection (AP) algorithm. The proposed expression explicitly shows the proportional relationship between the EMSE and the condition number of the input signals.

This paper introduces multiple view geometry under projective projection from four-dimensional space to two-dimensional space which can represent multiple view geometry under the projection of space-time. We show the multifocal tensors defined under space-time projective projection can be derived from non-rigid object motions viewed from multiple cameras with arbitrary translational motions, and they are practical for generating images of non-rigid object motions viewed from cameras with arbitrary translational motions. The method is tested in real image sequences.

In this paper we analytically investigate the generalization performance of learning using correlated inputs in the framework of on-line learning with a statistical mechanical method. We consider a model composed of linear perceptrons with Gaussian noise. First, we analyze the case of the gradient method. We analytically clarify that the larger the correlation among inputs is or the larger the number of inputs is, the stricter the condition the learning rate should satisfy is, and the slower the learning speed is. Second, we treat the block orthogonal projection learning as an alternative learning rule and derive the theory. In a noiseless case, the learning speed does not depend on the correlation and is proportional to the number of inputs used in an update. The learning speed is identical to that of the gradient method with uncorrelated inputs. On the other hand, when there is noise, the larger the correlation among inputs is, the slower the learning speed is and the larger the residual generalization error is.

This paper presents a closed form solution to a problem of constructing the best lower bound of a convex function under certain conditions. The function is assumed (I) bounded below by -ρ, and (II) differentiable and its derivative is Lipschitz continuous with Lipschitz constant L. To construct the lower bound, it is also assumed that we can use the values ρ and L together with the values of the function and its derivative at one specified point. By using the proposed lower bound, we derive a computationally efficient deep monotone approximation operator to the level set of the function. This operator realizes better approximation than subgradient projection which has been utilized, as a monotone approximation operator to level sets of differentiable convex functions as well as nonsmooth convex functions. Therefore, by using the proposed operator, we can improve many signal processing algorithms essentially based on the subgradient projection.

This paper proposes a new face recognition method based on mutual projection of feature distributions. The proposed method introduces a new robust measurement between two feature distributions. This measurement is computed by a harmonic mean of two distance values obtained by projection of each mean value into the opposite feature distribution. The proposed method does not require eigenvalue analysis of the two subspaces. This method was applied to face recognition task of temporal image sequence. Experimental results demonstrate that the computational cost was improved without degradation of identification performance in comparison with the conventional method.

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.

The character projection (CP) lithography is utilized for maskless lithography and is a potential for the future photomask fabrication. The drawback of the CP lithography is its low throughput and leads to a price rise of IC devices. This paper discusses a technology mapping technique for enhancing the throughput of the CP lithography. The number of electron beam (EB) shots to project an entire chip directly determines the fabrication time for the chip as well as the throughput of CP equipment. Our technology mapping technique maps EB shot count-effective cells to a circuit in order to increase the throughput of CP equipment. Our technique treats the number of EB shots as an objective to minimize. Comparing with a conventional technology mapping, our technology mapping technique has achieved 26.6% reduction of the number of EB shots for the front-end-of-the-line (FEOL) process without any performance degradation of ICs. Moreover, our technology mapping technique has achieved a 54.6% less number of EB shots under no performance constraints. It is easy for both IC designers and equipment developers to adopt our technique because our technique is a software approach with no additional modification on CP equipment.

We propose a gradient-limited affine projection algorithm (GL-APA), which can achieve fast and double-talk-robust convergence in acoustic echo cancellation. GL-APA is derived from the M-estimation-based nonlinear cost function extended for evaluating multiple error signals dealt with in the affine projection algorithm (APA). By considering the nonlinearity of the gradient, we carefully formulate an update equation consistent with multiple input-output relationships, which the conventional APA inherently satisfies to achieve fast convergence. We also newly introduce a scaling rule for the nonlinearity, so we can easily implement GL-APA by using a predetermined primary function as a basis of scaling with any projection order. This guarantees a linkage between GL-APA and the gradient-limited normalized least-mean-squares algorithm (GL-NLMS), which is a conventional algorithm that corresponds to the GL-APA of the first order. The performance of GL-APA is demonstrated with simulation results.