ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

ambiguity distance an edge evaluation measure using fuzziness of edges most edge detection methods have parameters threshold values or standard deviation of gaussian operator for smoothing to be set and these parameters make much influence on the outputs of the detectors in this paper we propose an objective parameter evaluation measure we evaluate parameters based on the edge ambiguity measures of existence location and formation the existence and location ambiguity measures are derived from comparing fuzzy memberships of edgeness with detected edges and the formation ambiguity measure assesses the connectedness and the total number of edge point in an edge image with respect to the image size the parameters which produce the least ambiguous edges of a detection method for an image are selected as significant ones no iterative visual interaction or prior knowledge of edges are needed for these evaluation measures the effectiveness of the measures is demonstrated by applying the ambiguity measures to synthetic and real images

sparse kernel regression modeling using combined locally regularized orthogonal least squares and d optimality experimental design the note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares lrols model selection with a d optimality experimental design the proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches the lrols method alone is capable of producing a very parsimonious model with excellent generalization performance the d optimality design criterion further enhances the model efficiency and robustness an added advantage is that the user only needs to specify a weighting for the d optimality cost in the combined model selecting criterion and the entire model construction procedure becomes automatic the value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values

feature selection using a piecewise linear network we present an efficient feature selection algorithm for the general regression problem which utilizes a piecewise linear orthonormal least squares ols procedure the algorithm 1 determines an appropriate piecewise linear network pln model for the given data set 2 applies the ols procedure to the pln model and 3 searches for useful feature subsets using a floating search algorithm the floating search prevents the nesting effect the proposed algorithm is computationally very efficient because only one data pass is required several examples are given to demonstrate the effectiveness of the proposed algorithm

fast orthogonal least squares algorithm for efficient subset model selection an efficient implementation of the orthogonal least squares algorithm for subset model selection is derived computational complexity of the algorithm is examined and the result shows that this new fast orthogonal least squares algorithm significantly reduces computational requirements

visible surface reconstruction via local minimax approximation abstract visible surface reconstruction is an important early stage in the processing and analysis of 3 d imagery as it provides a compact and manipulable representation of the 3 d structure of perceived objects in a scene in this paper we describe an algorithm for reconstructing visible surfaces from scattered surface depth orientation data using approximation methods the basic unit of the proposed algorithm is a minimax approximation routine which operates over regions of local surface support the minimax approach is attractive for several reasons and the computational cost is not high using fast algorithms a window based scheme is used to achieve a smooth surface reconstruction while maintaining discontinuities arising from object occlusions or sudden changes in surface orientation the discontinuities are detected as part of the algorithm results of the technique as applied to several test objects are provided

nonlinear model structure design and construction using orthogonal least squares and d optimality design a very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy the derived model parameters are estimated via forward orthogonal least squares but the model subset selection cost function includes a d optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness adequacy and parsimony of the final model the proposed approach is based on the forward orthogonal least square ols algorithm such that new d optimality based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward ols approach illustrative examples are included to demonstrate the effectiveness of the new approach

extended model set global data and threshold model identification of severely non linear systems abstract new parameter estimation algorithms based on an extended model set a global data model and a threshold model formulation are derived for identifying severely non linear systems it is shown that in each case an integrated structure determination and parameter estimation algorithm based on an orthogonal decomposition of the regression matrix can be derived to provide procedures for identifying parsimonious models of unknown systems with complex structure simulation studies are included to illustrate the techniques discussed

surface reconstruction and representation of 3 d scenes abstract this paper describes a method of reconstructing and representing the surface of objects in a 3 d scene from a set of parallel planar slices or cross sections the 3 d scene may consist of several occluding objects each slice may consist of a number of distinct 2 d regions defining the 2 d structure at that particular cross section the method described does not require that the scene description be a completely segmented one i e separate object structures need not be distinguished from each other the method can be used where only incomplete description due to missing data are available the generation of surface description consists of three steps first the contours of 2 d regions are traced and an attempt to segment the 3 d scene is made by associating contours on different slices second a triangulation process is performed over pairs of associated contours to generate the local bounding surface structure finally a surface hierarchy is established by coalescing adjacent triangular patches of same orientation into polygonal facets these facets are then integrated to form the object and scene description the surface structure thus obtained is a collection of polygonal facets which bound the outer surface of the objects

forward and backward least angle regression for nonlinear system identification a forward and backward least angle regression lar algorithm is proposed to construct the nonlinear autoregressive model with exogenous inputs narx that is widely used to describe a large class of nonlinear dynamic systems the main objective of this paper is to improve model sparsity and generalization performance of the original forward lar algorithm this is achieved by introducing a replacement scheme using an additional backward lar stage the backward stage replaces insignificant model terms selected by forward lar with more significant ones leading to an improved model in terms of the model compactness and performance a numerical example to construct four types of narx models namely polynomials radial basis function rbf networks neuro fuzzy and wavelet networks is presented to illustrate the effectiveness of the proposed technique in comparison with some popular methods

improving the generalization properties of radial basis function neural networks an important feature of radial basis function neural networks is the existence of a fast linear learning algorithm in a network capable of representing complex nonlinear mappings satisfactory generalization in these networks requires that the network mapping be sufficiently smooth we show that a modification to the error functional allows smoothing to be introduced explicitly without significantly affecting the speed of training a simple example is used to demonstrate the resulting improvement in the generalization properties of the network

a fast identification algorithm for box cox transformation based radial basis function neural network in this letter a box cox transformation based radial basis function rbf neural network is introduced using the rbf neural network to represent the transformed system output initially a fixed and moderate sized rbf model base is derived based on a rank revealing orthogonal matrix triangularization qr decomposition then a new fast identification algorithm is introduced using gauss newton algorithm to derive the required box cox transformation based on a maximum likelihood estimator the main contribution of this letter is to explore the special structure of the proposed rbf neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma finally the box cox transformation based rbf neural network with good generalization and sparsity is identified based on the derived optimal box cox transformation and a d optimality based orthogonal forward regression algorithm the proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression

recognizing cylindrical objects by single camera views a new approach to recognition of cylindrical objects by single camera views using camera calibration surface backprojection and model matching techniques is proposed cylindrical objects to be recognized can be of different radii and heights both the silhouette shapes and the surface patterns of objects are utilized in the recognition scheme a new camera calibration technique is first employed to compute the camera parameters analytically using a single camera view of the object a surface backprojection technique is then adopted to reconstruct the pattern on the surface patch of the input object the reconstructed surface pattern is finally matched with that of each object model using a partial shape matching technique to find the best matching surface patch pattern of the models from which the input object is classified accordingly experimental results showing the feasibility of the proposed approach are also included

incremental model building of polyhedral objects using structured light abstract a vision method using active sensing to construct the complete geometric model of a polyhedral object is presented the model is constructed incrementally from multiple views each view produces a partial object model three different methods are described for integrating all the partial models into a final complete model theorems regarding the sufficient number of views required and how these views can be set up during the reconstruction process are also given from theoretical analysis and experimental results our method is shown to produce an accurate object geometric model not just an approximate model furthermore it does not rely on a precise object to image space transformation moreover the method is fast and robust since the basic geometric entity it derives is a face instead of a point

context dependent edge detection and evaluation abstract to simulate the edge perception ability of human eyes and detect scene edges from an image context information must be employed in the edge detection process to accomplish the optimal use of context we introduce an edge detection scheme which uses the context of the whole image the edge context for each pixel is the set of all row monotonically increasing paths through the pixel the edge detector assigns a pixel that edge state having highest edge probability among all the paths based on the same framework we developed a general robust evaluator for edge detectors the scheme based on local edge coherence does not require any prior information about the ideal edge image and allows any size of neighborhood with which local edge coherence is evaluated on the basis of continuity thinness and positional accuracy the edge evaluator can be incorporated with a feedback mechanism to automatically adjust edge detection parameters e g edge thresholds for adaptive detection of edges in real images experiments indicate the validity of the edge detector and the general edge evaluator upon comparing the performance of the context dependent edge detector with the context free second directional derivative zero crossing edge operator we find that the context dependent edge detector is superior

curvature based fuzzy surface classification in this paper a fuzzy surface classification paradigm which is an extension to the conventional techniques based on the sign of the mean h and gaussian k curvatures respectively is presented with the conventional methods two of the major problems that limit object descriptions are 1 their inability to describe surfaces in a natural way and 2 computation of curvatures being highly sensitive to noise as well as limited by resolution problem 1 is addressed by treating the transitional regions between distinct surface types as smoothly varying fuzzy surface types problem 2 gets partially resolved while fuzzifying the signs of the surface curvatures for surface description the new segmentation technique is demonstrated in a model based object recognition system and its performance is compared with a system based on conventional surface classification

model selection and validation methods for non linear systems the theory of hypothesis testing is used to select a model with the correct structure and the relation of such a method to the aic and fpe criteria is investigated parametric validation and correlation validation methods are developed for non non linear difference equation models several shortcomings of traditional methods especially when applied to non linear systems are described

computation of surface orientation and structure of objects using grid coding in this correspondence algorithms are introduced to infer surface orientation and structure of visible object surfaces using grid coding we adopt the active lighting technique to spatially encode the scene for analysis the observed objects which can have surfaces of arbitrary shape are assumed to rest on a plane base plane in a scene which is encoded with light cast through a grid plane two orthogonal grid patterns are used where each pattern is obtained with a set of equally spaced stripes marked on a glass pane the scene is observed through a camera and the object surface orientation is determined using the projected patterns on the object surface if the surfaces under consideration obey certain smoothness constraints a dense orientation map can be obtained through proper interpolation the surface structure can then be recovered given this dense orientation map both planar and curved surfaces can be handled in a uniform manner the algorithms we propose yield reasonably accurate results and are relatively tolerant to noise especially when compared to shape from shading techniques in contrast to other grid coding techniques reported which match the grid junctions for depth reconstruction under the stereopsis principle our techniques use the direction of the projected stripes to infer local surface orientation and do not require any correspondence relationship between either the grid lines or the grid junctions to be specified the algorithm has the ability to register images and can therefore be embedded in a system which integrates knowledge from multiple views

separability criteria for the evaluation of boundary detection benchmarks there exist a significant number of benchmarks for evaluating the performance of boundary detection algorithms most of them relying on some sort of comparison of the automatically generated boundaries with human labeled ones such benchmarks are composed of a representative image data set as well as a comparison measure on the universe of boundary images despite many such data sets and measures have been proposed there is no clear way of knowing which combinations of them are the most suitable for the task in this paper we introduce four criteria that allow for a sensible evaluation of the performance of a comparison measure on a given data set the criteria mimic the way in which humans understand boundary images as well as their ability to recognize the underlying scenes these criteria can as a final goal quantify the ability of the boundary detection benchmarks to evaluate the performance of boundary detection methods either edge based or segmentation based

quantitative error measures for edge detection how to measure the performance of an edge detection method is an open problem many performance measures have been presented in the literature however there seems to be no agreement on the best option and there exist no practical studies of the features of some of the most recent measures in this work we make a comprehensive overview of the different proposals followed by a practical comparison of the most representative measures on synthetic as well as natural edge images

symmetric rbf classifier for nonlinear detection in multiple antenna aided systems in this paper we propose a powerful symmetric radial basis function rbf classifier for nonlinear detection in the so called overloaded multiple antenna aided communication systems by exploiting the inherent symmetry property of the optimal bayesian detector the proposed symmetric rbf classifier is capable of approaching the optimal classification performance using noisy training data the classifier construction process is robust to the choice of the rbf width and is computationally efficient the proposed solution is capable of providing a signal to noise ratio snr gain in excess of 8 db against the powerful linear minimum bit error rate ber benchmark when supporting four users with the aid of two receive antennas or seven users with four receive antenna elements

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

regularized orthogonal least squares algorithm for constructing radial basis function networks the paper presents a regularized orthogonal least squares learning algorithm for radial basis function networks the proposed algorithm combines the advantages of both the orthogonal forward regression and regularization methods to provide an efficient and powerful procedure for constructing parsimonious network models that generalize well examples of nonlinear modelling and prediction are used to demonstrate better generalization performance of this regularized orthogonal least squares algorithm over the unregularized one

experiments in computing optical flow with the gradient based multiconstraint method abstract in this paper we present results on experiments in computing optical flow with the multiconstraint approach this approach relies on the gradient equation which relates spatial and temporal changes in the image to optical flow and the use of various image functions the experiments reported here are performed on camera acquired pictures and use feature operators to derive image functions from the original luminance function results indicate that this approach is promising

sparse model identification using a forward orthogonal regression algorithm aided by mutual information a sparse representation with satisfactory approximation accuracy is usually desirable in any nonlinear system identification and signal processing problem a new forward orthogonal regression algorithm with mutual information interference is proposed for sparse model selection and parameter estimation the new algorithm can be used to construct parsimonious linear in the parameters models

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

least squares fitting of two 3 d point sets two point sets pi and p i i 1 2 n are related by p i rpi t ni where r is a rotation matrix t a translation vector and ni a noise vector given pi and p i we present an algorithm for finding the least squares solution of r and t which is based on the singular value decomposition svd of a 3 3 matrix this new algorithm is compared to two earlier algorithms with respect to computer time requirements

identification of space curves from two dimensional perspective views this paper describes a new method to be used for matching three dimensional objects with curved surfaces to two dimensional perspective views the method requires for each three dimensional object a stored model consisting of a closed space curve representing some characteristic connected curved edges of the object the input is a two dimensional perspective projection of one of the stored models represented by an ordered sequence of points the input is converted to a spline representation which is sampled at equal intervals to derive a curvature function the fourier transform of the curvature function is used to represent the shape the actual matching is reduced to a minimization problem which is handled by the levenberg marquardt algorithm 3

computational geometric methods in volumetric intersection for 3d reconstruction abstract generation and analysis of 3d models is an important task that enables automatic inspection placement and manipulation of physical objects by robotic systems this work presents a new approach to the generation of 3d models of arbitrarily shaped physical objects the models are generated from intensity images obtained from known view positions the objects are modelled by contours on successive parallel planes the model becomes more refined as more images are used the contour model supports the ability to generate the surface of an object by means of tessellation we have developed a model that supports efficient intersection not only to perform reconstruction but also to support inclusion testing and collision detection we have implemented this algorithm using images of real objects the algorithm s time complexity is linear with the number of views used and with the number of objects reconstructed the resolution of the algorithm in reconstructing the contours is limited only by machine precision constraints this is because the intersection points of the contours are determined analytically by solving sets of simultaneous equations which describe the line segments that compose the contours

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

matching three dimensional objects using silhouettes a method for matching three dimensional objects against a library of models from an observed sequence of silhouettes is presented in this correspondence based upon the observed silhouettes the three dimensional structure of the object is constructed and refined the principal moments and three primary silhouettes are computed for the constructed three dimensional objects to represent the aggregate and detailed structure parameters the adaptive matching technique requires that sufficient silhouettes be added to modify the structure of the unknown object until consistent and steady matching results are obtained the library for matching is based on three primary silhouettes of the model objects experiments conducted show a fast convergence to a consistent result may be achieved provided that a reasonable choice of silhouettes is made

the visual hull concept for silhouette based image understanding many algorithms for both identifying and reconstructing a 3 d object are based on the 2 d silhouettes of the object in general identifying a nonconvex object using a silhouette based approach implies neglecting some features of its surface as identification clues the same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object this paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette based image understanding for this purpose the geometric concept of visual hull of a 3 d object is introduced this is the closest approximation of object s that can be obtained with the volume intersection approach it is the maximal object silhouette equivalent to s i e which can be substituted for s without affecting any silhouette only the parts of the surface of s that also lie on the surface of the visual hull can be reconstructed or identified using silhouette based algorithms the visual hull depends not only on the object but also on the region allowed to the viewpoint two main viewing regions result in the external and internal visual hull in the former case the viewing region is related to the convex hull of s in the latter it is bounded by s the internal visual hull also admits an interpretation not related to silhouettes algorithms for computing visual hulls are presented and their complexity analyzed in general the visual hull of a 3 d planar face object turns out to be bounded by planar and curved patches

a kernel based two class classifier for imbalanced data sets many kernel classifier construction algorithms adopt classification accuracy as performance metrics in model evaluation moreover equal weighting is often applied to each data sample in parameter estimation these modeling practices often become problematic if the data sets are imbalanced we present a kernel classifier construction algorithm using orthogonal forward selection ofs in order to optimize the model generalization for imbalanced two class data sets this kernel classifier identification algorithm is based on a new regularized orthogonal weighted least squares rowls estimator and the model selection criterion of maximal leave one out area under curve loo auc of the receiver operating characteristics rocs it is shown that owing to the orthogonalization procedure the loo auc can be calculated via an analytic formula based on the new regularized orthogonal weighted least squares parameter estimator without actually splitting the estimation data set the proposed algorithm can achieve minimal computational expense via a set of forward recursive updating formula in searching model terms with maximal incremental loo auc value numerical examples are used to demonstrate the efficacy of the algorithm

polyhedron recognition using three view analysis abstract using three view analysis this paper proposes a new approach for single polyhedron recognition both the 3d surface data and 2d image projection patterns are used to find the exact corresponding model of an unknown input object the recognition process first applies a hypothesis generation verification process to match the 3d partial object of the unknown input which is reconstructed by applying the three view matching strategy chiou et al proc ics 88 pp 1516 1521 1988 and the polyhedron reconstruction process hung et al pattern recognition 22 231 246 1989 against the data based models for selecting the possible corresponding models candidates it then backprojects each candidate onto the three image planes and matches the outer boundaries of the three backprojections by a simple method for judging the exact corresponding model measurement error is also analyzed theoretically to give a bound of the threshold value so that it can be automatically chosen in each decision making process the approach is implemented on a pc level vision system experimental results show that the system is feasible and reliable even in a noisy environment

representations of non linear systems the narmax model abstract input output representations of non linear discrete time systems are discussed it is shown that the narmax non linear autoregressive moving average with exogenous inputs model is a general and natural representation of non linear systems and contains as special cases several existing non linear models the problem of approximating non linear input output systems is also addressed and several properties of non linear models are highlighted using simple examples