Localization of primitives using adaptive projections

An application of an active method in order to compute highly accurate D local ization of point features from few projections is presented The angle of projection of the image is controlled by the system and directed to extract D information from the environment in a manner leading to accurate location in less computation This model is relevant for tomographic reconstruction for feature based stereo and for model based robot registration Introduction Image analysis embraces a wide range of image processing tasks including object local ization and identi cation Traditional approachs to these tasks have entailed a passive approach to the data collection problem the main emphasis being on the algorithms to ex tract the exact information from the images already taken The full llment of computer vision tasks is based on analysis of a given image or image sequence The recognition process has no control over the imaging process The results usually have no reliability measure associated with them Consequently current systems are often characterized by such shortcomings as problems with uniqueness accuracy and or stability An active approach to the imaging process is advocated in order to achieve more robust and reliable results using less computation Active vision as referred to in this paper is input dependent data acquisition coupled with a treatment of the reliability of the acquired information A mathematical model is proposed that includes the known information in the scene and the expected information to be sensed by the system From the model a new optimal sensing position is determined A picture taken from this new position should enable the system to deduce as much new D information as possible Generally the D information is composed of location in space and its certainty Intelli gent active perception includes algorithms for updating the known information according to the input positioning the sensor and judging the reliability of the information that the Y H was supported by the Leibniz Center for Reseach in Computer Science system already has Kalman ltering techniques are used for updating information as Kalman ltering is an optimal method of integrating data The proposed approach contributes to the following problems improving the stability of solutions and the ability to perform tasks in a noisy environment improving exactness and reliability of solutions and reducing the quantity of data needed and the time for its analysis Reducing the amount of necessary data and speeding its analysis is a side e ect of gathering only the information needed to complete the computation rather than collecting information in a random manner There has been some previous work done using active vision as a model for robot vision using di erent aspects of vision such as vergence stereo xation and focus in a human like manner These papers treat the control activation and reinforcement of certain of the sensing modes on the others This paper describes an application of the active method in order to compute highly accurate D localization of point features from few projections The angle of projection of the image is controlled by the system and directed to extract D information from the environment in a manner leading to accurate location on less computation After each phase of computation between projections the information already computed is assessed and when information is still needed a new optimal angle for the next projection is derived This process repeatedly takes place until a su cient accuracy is achieved in the solution This model is relevant for tomographic reconstraction and for robot registration based on scene model Section contains an introduction of the Gauss Markov model and the Kalman lter Sections and treat the and D cases in detail The imaging model and the compu tation of optimal angle for the next projection are described Simulation results are given in section The Static Gauss Markov Model and the Kalman Filter The Static Gauss Markov discrete time model is a particular case of the general Gauss Markov Model and describes a class of physical or abstract systems The state of the system is described by a nite dimensional vector s This state is measured at time t by mt which is the result of a linear transformation H T t of the state contaminated by an additive noise process vt mt H T t s vt vt N Rt The subscript t denotes a time argument The noise process is described as a zero mean Gaussian process with known covariance matrix Rt It is characterized as a white process in the sense that for any two di erent time instants k and l vk and vl are independent random variables For the model described above the static Kalman lter is a method for optimally estimating the system state by using the measurements recorded up to the current time Current estimation of the system state st is in e ect the conditional expectance st E sjm m mt for t X for any X means the estimated X The quality of this estimate is given by the error covariance matrix t E s st s st T jm m mt for t The Kalman lter is an unbiased estimator and in addition to that it is optimal with respect to the minimum variance criteria trace t E jjs stjj jm m mt for t is the conditional error variance associated with the estimate st and st E stjm m mt minimizes this error variance The explicit state update and error covariance matrix update euations describing one step of the static Kalman lter are st st tHt H T t tHt Rt mt H T t st t t tHt H T t tHt Rt H t t s and are assumed to be known due to prior knowledge The incremental character of the equations enables the extraction of all the information realized by previous measurements by using the estimation and variance corresponding to the current time Further description of both the Gauss Markov model and the Kalman lter can be found in Uncertainty Driven Active Projection Optimal Positioning of a Single Feature The model described through this section is concerned with the D plane speci ed by the Cartesian coordinates X Y Let F be a feature point in the D plane The position of F PF is uncertain and modelled in time t as a bivariate Gaussian random vector PF XF YF N PF t F t where PF t XF YF t and F t xx xy xy yy t are the current estimation of the position of F and the covariance matrix that evaluates this estimation