elastically adaptive deformable models we present a technique for the automatic adaptation of a deformable model s elastic parameters within a kalman filter framework for shape estimation applications the novelty of the technique is that the model s elastic parameters are not constant but spatio temporally varying the variation of the elastic parameters depends on the distance of the model from the data and the rate of change of this distance each pass of the algorithm uses physics based modeling techniques to iteratively adjust both the geometric and the elastic degrees of freedom of the model in response to forces that are computed from the discrepancy between the model and the data by augmenting the state equations of an extended kalman filter to incorporate these additional variables we are able to significantly improve the quality of the shape estimation therefore the model s elastic parameters are always initialized to the same value and they are subsequently modified depending on the data and the noise distribution we present results demonstrating the effectiveness of our method for both two dimensional and three dimensional data

direct transformation of nonlinear systems into state affine miso form for observer design this paper gives necessary and sufficient conditions to solve in a constructive way the transformation of a general multiple input single output nonlinear system into a state affine system this result is direct i e without solving the state elimination problem when computing the input output differential equation a kalman like observer can be designed for the obtained state affine system

3d structure recovery and unwarping of surfaces applicable to planes the deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry lengths and areas are conserved and vanishing gaussian curvature we show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape we show that these partial differential equations can be reduced to the hopf equation that arises in non linear wave propagation and deformations of the paper can be interpreted in terms of the characteristics of this equation a new exact integration of these equations is developed that relates the 3 d structure of the applicable surface to an image the solution is tested by comparison with particular exact solutions we present results for both the forward and the inverse 3d structure recovery problem

surface reconstruction using deformable models with interior and boundary constraints the authors introduce a technique for 3d surface reconstruction using elastic deformable models the model used is an imaginary elastic grid which is made of membranous thin plate type material the elastic grid can bent twisted compressed and stretched into any desired 3d shape which is specified by the shape constraints derived automatically from images of a real 3d object shape reconstruction is guided by a set of imaginary springs that enforce the consistency in the position orientation and or curvature measurements of the elastic grid and the desired shape the dynamics of a surface reconstruction process is regulated by hamilton s principle or the principle of the least action furthermore a 1d deformable template that borders the elastic grid may be used this companion boundary template is attracted repelled by image forces to conform with the silhouette of the imaged object implementation results using simple analytic shapes and images of real objects are presented

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

a new procedure for time varying linearization up to output injection new necessary and sufficient conditions for time varying linearization up to output injection tvloi are presented they yield a straightforward tvloi procedure

on nonlinear continuous observers the paper investigates the possibility of using smooth maps with continuous inverses which are called semi diffeomorphisms here for the study of observability and observer design for nonlinear smooth systems a method is proposed for the design of continuous observers for uniformly observable nonlinear systems the results obtained also cover systems not coverable by all previous results on smooth nonlinear observers

constraints on deformable models recovering 3d shape and nongrid motion abstract inferring the 3d structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision our approach makes use of dynamic elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real world visual constraints we specialize these models to include intrinsic forces inducing a preference for axisymmetry image based constraints are applied as extrinsic forces that mold the symmetry seeking model into shapes consistent with image data we describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects we generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data for time varying images the force becomes dynamic and the model is able to infer not only depth but nonrigid motion as well we demonstrate the recovery of 3d shape and nonrigid motion from natural imagery

global time varying linearization up to output injection this paper following the purpose of synthesis of observers for nonlinear systems investigates the question of equivalence of a nonlinear system with a bilinear system or more generally a linear time dependent system plus an output injection in a previous work by the same authors such questions have already been dealt with from the local point of view the goal herein is to examine the global situation using basic facts from algebraic topology it is shown that in the single output case whenever the possibility to bilinearize up to output injection holds locally everywhere it also holds globally

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

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

law of large numbers for non local functions on probabilistic cellular automata we prove a multi dimensional version of the law of large numbers for invariant measures of a large class of probabilistic cellular automata whose transition probabilities satisfy some inequalities which are known to assure their ergodicity in some non ergodic cases analogous results have been obtained for local functions we deal with a larger class of functions which includes some non local ones

representation and shape matching of 3 d objects a three dimensional scene analysis system for the shape matching of real world 3 d objects is presented various issues related to representation and modeling of 3 d objects are addressed a new method for the approximation of 3 d objects by a set of planar faces is discussed the major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the limitation of the previous work in 3 d scene analysis the method is a sequential region growing algorithm it is not applied to range images but rather to a set of 3 d points the 3 d model of an object is obtained by combining the object points from a sequence of range data images corresponding to various views of the object applying the necessary transformations and then approximating the surface by polygons a stochastic labeling technique is used to do the shape matching of 3 d objects the technique matches the faces of an unknown view against the faces of the model it explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification it is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels the objective here is to match the individual views of the object taken from any vantage point details of the algorithm are presented and the results are shown on several unknown views of a complicated automobile casting

characterizing three dimensional surface structures from visual images a new technique for computing intrinsic surface properties is presented intrinsic surface properties are those properties of a surface that are not affected by the choice of the coordinate system the position of the viewer relative to the surface and the particular parametric representation used to describe the imaged surface since intrinsic properties are characteristics of a surface they are ideal for the purposes of representation and recognition the intrinsic properties of interest are the principal curvatures the gaussian curvatures and the lines of curvature it is proposed that a structured light sensing configuration where a grid pattern is projected to encode the imaged surfaces for analysis be adopted at each stripe junction the curvatures of the projected stripes on the imaged surface are computed and related to those of the normal sections that share the same tangential directional as the projected curves the principal curvatures and their directions at the stripe junction under consideration are then recovered using euler s theorem results obtained using both synthetic and real images are presented

determining surface orientation by projecting a stripe pattern a method is presented for determining the surface orientations of an object by projecting a stripe pattern on to it assuming orthographical projection as a camera model and parallel light projection of the stripe pattern the method obtains a 2 1 2 d representation of objects by estimating surface normals from the slopes and intervals of the stripes in the image the 2 1 2 d image is further divided into planar or singly curved surfaces by examining the distribution of the surface normals in gradient space a simple application to finding a planar surface and determining its orientation and shape is shown the error in surface orientation is discussed

error analysis of 3d shape construction from structured lighting abstract in this paper we present a detailed model and analysis of several error sources and thier effects on measuring three dimensional 3d surface properties using the structured lighting technique the analysis is based on a general system configuration and identifies three types of error surces system modeling error image processing error and experimental error absolute and relative error bounds in obtaining 3d surface orientation and curvature measurements using structured lighting are derived in terms of the system parameters and likely error sources in addition to the quantization error other likely error sources in system modeling and experimental setup are also considered even though our analysis is on structured lighting the results are readily applicable to other triangulation based techniques such as stereopsis finally our analysis focuses on error in inferring surface orientation and principal surface curvature such analyses to our knowledge have never been attempted before

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

on output transformations for state linearization up to output injection steering a nonlinear system into a so called state affine one up to output injection by change of coordinates is of much interest for observer design this interest is preserved by also considering changes of output the purpose of the paper is then to provide computable conditions for existence of output transformations making a system which is not transformable into a state affine one up to output injection by only a change of coordinates to become so after a change of output such a characterization enlarges the class of systems for which an observer is available

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

bilinearization up to output injection abstract this paper deals with nonlinear systems that can be steered to bilinear systems by output injection and nonlinear change of coordinates we give an abstract non constructive theorem and an algorithm which allows us to recognize such systems

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

symbolic computing of nonlinear observable and observer forms observer design for highly nonlinear dynamics is an important issue particularly when the locally observable dynamics are not linearly observable in such circumstances the ability to reduce the system to observable or observer form is a useful first step to observer design we describe and illustrate symbolic computing tools to do that

surface orientation from a projected grid two simple methods are given for obtaining the surface shape using a projected grid after the camera is calibrated to the 3 d workspace the only input date needed for the computation of surface normals are grid intersect points in a single 2 d image the first method performs nonlinear computations based on the distortion of the lengths of the grid edges and does not require a full calibration matrix the second method requires that a full parallel projection model of the imaging is available which enables it to compute 3 d normals using simple linear computations the linear method performed better overall in the experiments but both methods produced normals within 4 8 degrees of known 3 d directions these methods appear to be superior to methods based on shape from shading because the results are comparable yet the equipment setup is simpler and the processing is not very sensitive to object reflectance

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

constructing intrinsic parameters with active models for invariant surface reconstruction a technique for constructing a canonical surface parameterization in terms of lines of curvature is presented two methods of computing the canonical invariant representation are also presented in the first method a static instance of the controlled continuity spline is used for the stabilizer ways to modify it to reflect a change of parameters to the lines of curvature are described in the second method the dynamic instance of the controlled continuity spline called the deformable model is used a force field defined in terms of the principal vectors is synthesized and applied to the parameter curves of the deformable model to coerce them along the lines of curvature in essence any transformation of parameters requires a modification of the stabilizer in the first method whereas in the second method it is tantamount to synthesizing a new force field experimental results with real and synthetic range data are included

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

structured light using pseudorandom codes we solve the correspondence problem in active stereo vision using a novel pseudorandom coded structured light sl this coding scheme performs well in the presence of occlusion in settings where color coding is feasible 3d information can be obtained using a single image

shape and nonrigid motion estimation through physics based synthesis a physics based framework for 3 d shape and nonrigid motion estimation for real time computer vision systems is presented the framework features dynamic models that incorporate the mechanical principles of rigid and nonrigid bodies into conventional geometric primitives through the efficient numerical simulation of lagrange equations of motion the models can synthesize physically correct behaviors in response to applied forces and imposed constraints applying continuous kalman filtering theory a recursive shape and motion estimator that employs the lagrange equations as a system model is developed the system model continually synthesizes nonrigid motion in response to generalized forces that arise from the inconsistency between the incoming observations and the estimated model state the observation forces also account formally for instantaneous uncertainties and incomplete information a riccati procedure updates a covariance matrix that transforms the forces in accordance with the system dynamics and prior observation history experiments involving model fitting and tracking of articulated and flexible objects from noisy 3 d data are described

numerical shape from shading and occluding boundaries an iterative method for computing shape from shading using occluding boundary information is proposed some applications of this method are shown we employ the stereographic plane to express the orientations of surface patches rather than the more commonly used gradient space use of the stereographic plane makes it possible to incorporate occluding boundary information but forces us to employ a smoothness constraint different from the one previously proposed the new constraint follows directly from a particular definition of surface smoothness we solve the set of equations arising from the smoothness constraints and the image irradiance equation iteratively using occluding boundary information to supply boundary conditions good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution numerical experiments show that the method is effective and robust finally we analyze scanning electron microscope sem pictures using this method other applications are also proposed

statistical mechanics of surjective cellular automata reversible cellular automata are seen as microscopic physical models and their states of macroscopic equilibrium are described using invariant probability measures we establish a connection between the invariance of gibbs measures and the conservation of additive quantities in surjective cellular automata namely we show that the simplex of shift invariant gibbs measures associated to a hamiltonian is invariant under a surjective cellular automaton if and only if the cellular automaton conserves the hamiltonian a special case is the well known invariance of the uniform bernoulli measure under surjective cellular automata which corresponds to the conservation of the trivial hamiltonian as an application we obtain results indicating the lack of non trivial gibbs or markov invariant measures for sufficiently chaotic cellular automata we discuss the relevance of the randomization property of algebraic cellular automata to the problem of approach to macroscopic equilibrium and pose several open questions as an aside a shift invariant pre image of a gibbs measure under a pre injective factor map between shifts of finite type turns out to be always a gibbs measure we provide a sufficient condition under which the image of a gibbs measure under a pre injective factor map is not a gibbs measure we point out a potential application of pre injective factor maps as a tool in the study of phase transitions in statistical mechanical models

the visual interpretation of surface contours this article examines the computational problems underlying the 3 d interpretation of surface contours a surface contour is the image of a curve across a physical surface such as the edge of a shadow cast across a surface a gloss contour wrinkle seam or pigmentation marking surface contours by and large are not as restricted as occluding contours and therefore pose a more difficult interpretation problem nonetheless we are adept at perceiving a definite 3 d surface from even simple line drawings e g graphical depictions of continuous functions of two variables the solution of a specific surface shape comes by assuming that the physical curves are particularly restricted in their geometric relationship to the underlying surface these geometric restrictions are examined

observer with linear error dynamics for nonlinear multi output systems based upon nonlinear state coordinate transformations and a condensed dual brunovsk form for multi output systems a method for designing nonlinear state observers with linear error dynamics is presented necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained

detection of rotationally symmetric shape orientations by fold invariant shape specific points abstract two new types of shape specific points called fold invariant centroid fic and fold invariant radius weighted mean firwm are introduced for detecting the orientations of rotationally symmetric shapes a given rotationally symmetric shape is first transformed into a new fold invariant shape the centroid and the radius weighted mean of the new shape are then transformed back to obtain the proposed fic and firwm respectively fic and firwm points are proved to be invariant to translation rotation and scaling and so can be used for matching rotationally symmetric shapes using the proposed fold invariant shape specific points to detect the orientations of rotationally symmetric shapes is easier to implement than that of using the fold principal axes some illustrative examples and a method to avoid the case where the proposed fold invariant shape specific points are too close to the centroid are also given

an algebraic approach to shape from image problems abstract this paper presents a new method for recovering three dimensional shapes of polyhedral objects from their single view images the problem of recovery is formulated in a constrained optimization problem in which the constraints reflect the assumption that the scene is composed of polyhedral objects and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture for practical purpose it is decomposed into the two more tractable problems a linear programming problem and an unconstrained optimization problem in the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra whereas similar constraints have usually been represented in terms of a gradient space moreover superstrictness of the constraints can be circumvented by a new concept position free incidence structure for this reason the present method has several advantages it can recover the polyhedral shape even if image data are incorrect due to vertex position errors it can deal with perspective projection as well as orthographic projection the number of variables in the optimization problem is very small three or a little greater than three and any kinds of surface information can be incorporated in a unifying manner