Sensor Fusion and its Applications Part 4 doc

Sensor Fusion and Its Applications84 INS GPS KF + - measurement prediction )( * xh ATS + + x GPS x INS Determination of P λ and R λ Estimated INS Errors Corrected output x ˆ Innovation information Fig. 10. GPS/INS navigation processing using the IAE/AFKF Hybrid AKF for the illustrative example 2 Fig. 11. Trajectory for the simulated vehicle (solid) and the INS derived position (dashed) Fig. 12. The solution from the integrated navigation system without adaptation as compared to the GPS navigation solutions by the LS approach Fig. 13. The solutions for the integrated navigation system with and without adaptation In the real world, the measurement will normally be changing in addition to the change of process noise or dynamic such as maneuvering. In such case, both P-adaptation and R- adaptation tasks need to be implemented. In the following discussion, results will be provided for the case when measurement noise strength is changing in addition to the Adaptive Kalman Filter for Navigation Sensor Fusion 85 INS GPS KF + - measurement prediction )( * xh ATS + + x GPS x INS Determination of P λ and R λ Estimated INS Errors Corrected output x ˆ Innovation information Fig. 10. GPS/INS navigation processing using the IAE/AFKF Hybrid AKF for the illustrative example 2 Fig. 11. Trajectory for the simulated vehicle (solid) and the INS derived position (dashed) Fig. 12. The solution from the integrated navigation system without adaptation as compared to the GPS navigation solutions by the LS approach Fig. 13. The solutions for the integrated navigation system with and without adaptation In the real world, the measurement will normally be changing in addition to the change of process noise or dynamic such as maneuvering. In such case, both P-adaptation and R- adaptation tasks need to be implemented. In the following discussion, results will be provided for the case when measurement noise strength is changing in addition to the Sensor Fusion and Its Applications86 change of process noise strength. The measurement noise strength is assumed to be changing with variances of the values 2222 38164 r , where the ‘arrows (→)’ is employed for indicating the time-varying trajectory of measurement noise statistics. That is, it is assumed that the measure noise strength is changing during the four time intervals: 0- 450s ( )4,0( 2 N ), 451-900s ( )16,0( 2 N ), 901-1350s ( )8,0( 2 N ), and 1351-1800s ( )3,0( 2 N ). However, the internal measurement noise covariance matrix k R is set unchanged all the time in simulation, which uses )3,0(~ 2 Nr j , nj ,2,1  , at all the time intervals. Fig. 14 shows the east and north components of navigation errors and the 1-σ bound based on the method without adaptation on measurement noise covariance matrix. It can be seen that the adaptation of P information without correct R information (referred to partial adaptation herein) seriously deteriorates the estimation result. Fig. 15 provides the east and north components of navigation errors and the 1-σ bound based on the proposed method (referred to full adaptation herein, i.e., adaptation on both estimation covariance and measurement noise covariance matrices are applied). It can be seen that the estimation accuracy has been substantially improved. The measurement noise strength has been accurately estimated, as shown in Fig. 16. Fig. 14. East and north components of navigation errors and the 1-σ bound based on the method without measurement noise adaptation It should also be mentioned that the requirement 1)(  iiP λ is critical. An illustrative example is given in Figs. 17 and 18. Fig. 17 gives the navigation errors and the 1-σ bound when the threshold setting is not incorporated. The corresponding reference (true) and calculated standard deviations when the threshold setting is not incorporated is provided in Fig. 18. It is not surprising that the navigation accuracy has been seriously degraded due to the inaccurate estimation of measurement noise statistics. Partial adaptation Partial adaptation Fig. 15. East and north components of navigation errors and the 1-σ bound based on the proposed method (with adaptation on both estimation covariance and measurement noise covariance matrices) Fig. 16. Reference (true) and calculated standard deviations for the east (top) and north (bottom) components of the measurement noise variance values Full adaptation Full adaptation Reference (dashed) Calculated (solid) Calculated (solid) Reference (dashed) Adaptive Kalman Filter for Navigation Sensor Fusion 87 change of process noise strength. The measurement noise strength is assumed to be changing with variances of the values 2222 38164 r , where the ‘arrows (→)’ is employed for indicating the time-varying trajectory of measurement noise statistics. That is, it is assumed that the measure noise strength is changing during the four time intervals: 0- 450s ( )4,0( 2 N ), 451-900s ( )16,0( 2 N ), 901-1350s ( )8,0( 2 N ), and 1351-1800s ( )3,0( 2 N ). However, the internal measurement noise covariance matrix k R is set unchanged all the time in simulation, which uses )3,0(~ 2 Nr j , nj ,2,1   , at all the time intervals. Fig. 14 shows the east and north components of navigation errors and the 1-σ bound based on the method without adaptation on measurement noise covariance matrix. It can be seen that the adaptation of P information without correct R information (referred to partial adaptation herein) seriously deteriorates the estimation result. Fig. 15 provides the east and north components of navigation errors and the 1-σ bound based on the proposed method (referred to full adaptation herein, i.e., adaptation on both estimation covariance and measurement noise covariance matrices are applied). It can be seen that the estimation accuracy has been substantially improved. The measurement noise strength has been accurately estimated, as shown in Fig. 16. Fig. 14. East and north components of navigation errors and the 1-σ bound based on the method without measurement noise adaptation It should also be mentioned that the requirement 1)(  iiP λ is critical. An illustrative example is given in Figs. 17 and 18. Fig. 17 gives the navigation errors and the 1-σ bound when the threshold setting is not incorporated. The corresponding reference (true) and calculated standard deviations when the threshold setting is not incorporated is provided in Fig. 18. It is not surprising that the navigation accuracy has been seriously degraded due to the inaccurate estimation of measurement noise statistics. Partial adaptation Partial adaptation Fig. 15. East and north components of navigation errors and the 1-σ bound based on the proposed method (with adaptation on both estimation covariance and measurement noise covariance matrices) Fig. 16. Reference (true) and calculated standard deviations for the east (top) and north (bottom) components of the measurement noise variance values Full adaptation Full adaptation Reference (dashed) Calculated (solid) Calculated (solid) Reference (dashed) Sensor Fusion and Its Applications88 Fig. 17. East and north components of navigation errors and the 1-σ bound based on the proposed method when the threshold setting is not incorporated Fig. 18. Reference (true) and calculated standard deviations for the east and north components of the measurement noise variance values when the threshold setting is not incorporated Reference (dashed) Calculated ( solid ) Calculated (solid) Reference (dashed) 5. Conclusion This chapter presents the adaptive Kalman filter for navigation sensor fusion. Several types of adaptive Kalman filters has been reviewed, including the innovation-based adaptive estimation (IAE) approach and the adaptive fading Kalman filter (AFKF) approach. Various types of designs for the fading factors are discussed. A new strategy through the hybridization of IAE and AFKF is presented with an illustrative example for integrated navigation application. In the first example, the fuzzy logic is employed for assisting the AFKF. Through the use of fuzzy logic, the designed fuzzy logic adaptive system (FLAS) has been employed as a mechanism for timely detecting the dynamical changes and implementing the on-line tuning of threshold c , and accordingly the fading factor, by monitoring the innovation information so as to maintain good tracking capability. In the second example, the conventional KF approach is coupled by the adaptive tuning system (ATS), which gives two system parameters: the fading factor and measurement noise covariance scaling factor. The ATS has been employed as a mechanism for timely detecting the dynamical and environmental changes and implementing the on-line parameter tuning by monitoring the innovation information so as to maintain good tracking capability and estimation accuracy. Unlike some of the AKF methods, the proposed method has the merits of good computational efficiency and numerical stability. The matrices in the KF loop are able to remain positive definitive. Remarks to be noted for using the method is made, such as: (1) The window sizes can be set different, to avoid the filter degradation/divergence; (2) The fading factors iiP )(λ should be always larger than one while jjR )(λ does not have such limitation. Simulation experiments for navigation sensor fusion have been provided to illustrate the accessibility. The accuracy improvement based on the AKF method has demonstrated remarkable improvement in both navigational accuracy and tracking capability. 6. References Abdelnour, G.; Chand, S. & Chiu, S. (1993). Applying fuzzy logic to the Kalman filter divergence problem. IEEE Int. Conf. On Syst., Man and Cybernetics, Le Touquet, France, pp. 630-634 Brown, R. G. & Hwang, P. Y. C. (1997). Introduction to Random Signals and Applied Kalman Filtering, John Wiley & Sons, New York, 3 rd edn Bar-Shalom, Y.; Li, X. R. & Kirubarajan, T. (2001). Estimation with Applications to Tracking and Navigation, John Wiley & Sons, Inc Bakhache, B. & Nikiforov, I. (2000). Reliable detection of faults in measurement systems, International Journal of adaptive control and signal processing, 14, pp. 683-700 Caliskan, F. & Hajiyev, C. M. (2000). Innovation sequence application to aircraft sensor fault detection: comparison of checking covariance matrix algorithms, ISA Transactions, 39, pp. 47-56 Ding, W.; Wang, J. & Rizos, C. (2007). Improving Adaptive Kalman Estimation in GPS/INS Integration, The Journal of Navigation, 60, 517-529. Farrell, I. & Barth, M. (1999) The Global Positioning System and Inertial Navigation, McCraw- Hill professional, New York Gelb, A. (1974). Applied Optimal Estimation. M. I. T. Press, MA. Adaptive Kalman Filter for Navigation Sensor Fusion 89 Fig. 17. East and north components of navigation errors and the 1-σ bound based on the proposed method when the threshold setting is not incorporated Fig. 18. Reference (true) and calculated standard deviations for the east and north components of the measurement noise variance values when the threshold setting is not incorporated Reference (dashed) Calculated ( solid ) Calculated (solid) Reference (dashed) 5. Conclusion This chapter presents the adaptive Kalman filter for navigation sensor fusion. Several types of adaptive Kalman filters has been reviewed, including the innovation-based adaptive estimation (IAE) approach and the adaptive fading Kalman filter (AFKF) approach. Various types of designs for the fading factors are discussed. A new strategy through the hybridization of IAE and AFKF is presented with an illustrative example for integrated navigation application. In the first example, the fuzzy logic is employed for assisting the AFKF. Through the use of fuzzy logic, the designed fuzzy logic adaptive system (FLAS) has been employed as a mechanism for timely detecting the dynamical changes and implementing the on-line tuning of threshold c , and accordingly the fading factor, by monitoring the innovation information so as to maintain good tracking capability. In the second example, the conventional KF approach is coupled by the adaptive tuning system (ATS), which gives two system parameters: the fading factor and measurement noise covariance scaling factor. The ATS has been employed as a mechanism for timely detecting the dynamical and environmental changes and implementing the on-line parameter tuning by monitoring the innovation information so as to maintain good tracking capability and estimation accuracy. Unlike some of the AKF methods, the proposed method has the merits of good computational efficiency and numerical stability. The matrices in the KF loop are able to remain positive definitive. Remarks to be noted for using the method is made, such as: (1) The window sizes can be set different, to avoid the filter degradation/divergence; (2) The fading factors iiP )(λ should be always larger than one while jjR )(λ does not have such limitation. Simulation experiments for navigation sensor fusion have been provided to illustrate the accessibility. The accuracy improvement based on the AKF method has demonstrated remarkable improvement in both navigational accuracy and tracking capability. 6. References Abdelnour, G.; Chand, S. & Chiu, S. (1993). Applying fuzzy logic to the Kalman filter divergence problem. IEEE Int. Conf. On Syst., Man and Cybernetics, Le Touquet, France, pp. 630-634 Brown, R. G. & Hwang, P. Y. C. (1997). Introduction to Random Signals and Applied Kalman Filtering, John Wiley & Sons, New York, 3 rd edn Bar-Shalom, Y.; Li, X. R. & Kirubarajan, T. (2001). Estimation with Applications to Tracking and Navigation, John Wiley & Sons, Inc Bakhache, B. & Nikiforov, I. (2000). Reliable detection of faults in measurement systems, International Journal of adaptive control and signal processing, 14, pp. 683-700 Caliskan, F. & Hajiyev, C. M. (2000). Innovation sequence application to aircraft sensor fault detection: comparison of checking covariance matrix algorithms, ISA Transactions, 39, pp. 47-56 Ding, W.; Wang, J. & Rizos, C. (2007). Improving Adaptive Kalman Estimation in GPS/INS Integration, The Journal of Navigation, 60, 517-529. Farrell, I. & Barth, M. (1999) The Global Positioning System and Inertial Navigation, McCraw- Hill professional, New York Gelb, A. (1974). Applied Optimal Estimation. M. I. T. Press, MA. Sensor Fusion and Its Applications90 Grewal, M. S. & Andrews, A. P. (2001). Kalman Filtering, Theory and Practice Using MATLAB, 2 nd Ed., John Wiley & Sons, Inc. Hide, C, Moore, T., & Smith, M. (2003). Adaptive Kalman filtering for low cost INS/GPS, The Journal of Navigation, 56, 143-152 Jwo, D J. & Cho, T S. (2007). A practical note on evaluating Kalman filter performance Optimality and Degradation. Applied Mathematics and Computation, 193, pp. 482-505 Jwo, D J. & Wang, S H. (2007). Adaptive fuzzy strong tracking extended Kalman filtering for GPS navigation, IEEE Sensors Journal, 7(5), pp. 778-789 Jwo, D J. & Weng, T P. (2008). An adaptive sensor fusion method with applications in integrated navigation. The Journal of Navigation, 61, pp. 705-721 Jwo, D J. & Chang, F I., 2007, A Fuzzy Adaptive Fading Kalman Filter for GPS Navigation, Lecture Notes in Computer Science, LNCS 4681:820-831, Springer-Verlag Berlin Heidelberg. Jwo, D J. & Huang, C. M. (2009). A Fuzzy Adaptive Sensor Fusion Method for Integrated Navigation Systems, Advances in Systems Science and Applications, 8(4), pp.590-604. Loebis, D.; Naeem, W.; Sutton, R.; Chudley, J. & Tetlow S. (2007). Soft computing techniques in the design of a navigation, guidance and control system for an autonomous underwater vehicle, International Journal of adaptive control and signal processing, 21:205-236 Mehra, R. K. (1970). On the identification of variance and adaptive Kalman filtering. IEEE Trans. Automat. Contr., AC-15, pp. 175-184 Mehra, R. K. (1971). On-line identification of linear dynamic systems with applications to Kalman filtering. IEEE Trans. Automat. Contr., AC-16, pp. 12-21 Mehra, R. K. (1972). Approaches to adaptive filtering. IEEE Trans. Automat. Contr., Vol. AC- 17, pp. 693-698 Mohamed, A. H. & Schwarz K. P. (1999). Adaptive Kalman filtering for INS/GPS. Journal of Geodesy, 73 (4), pp. 193-203 Mostov, K. & Soloviev, A. (1996). Fuzzy adaptive stabilization of higher order Kalman filters in application to precision kinematic GPS, ION GPS-96, Vol. 2, pp. 1451-1456, Kansas Salychev, O. (1998). Inertial Systems in Navigation and Geophysics, Bauman MSTU Press, Moscow. Sasiadek, J. Z.; Wang, Q. & Zeremba, M. B. (2000). Fuzzy adaptive Kalman filtering for INS/GPS data fusion. 15 th IEEE int. Symp. on intelligent control, Rio Patras, Greece, pp. 181-186 Xia, Q.; Rao, M.; Ying, Y. & Shen, X. (1994). Adaptive fading Kalman filter with an application, Automatica, 30, pp. 1333-1338 Yang, Y.; He H. & Xu, T. (1999). Adaptively robust filtering for kinematic geodetic positioning, Journal of Geodesy, 75, pp.109-116 Yang, Y. & Xu, T. (2003). An adaptive Kalman filter based on Sage windowing weights and variance components, The Journal of Navigation, 56(2), pp. 231-240 Yang, Y.; Cui, X., & Gao, W. (2004). Adaptive integrated navigation for multi-sensor adjustment outputs, The Journal of Navigation, 57(2), pp. 287-295 Zhou, D. H. & Frank, P. H. (1996). Strong tracking Kalman filtering of nonlinear time- varying stochastic systems with coloured noise: application to parameter estimation and empirical robustness analysis. Int. J. control, Vol. 65, No. 2, pp. 295- 307 Fusion of Images Recorded with Variable Illumination 91 Fusion of Images Recorded with Variable Illumination Luis Nachtigall, Fernando Puente León and Ana Pérez Grassi 0 Fusion of Images Recorded with Variable Illumination Luis Nachtigall and Fernando Puente León Karlsruhe Institute of Technology Germany Ana Pérez Grassi Technische Universität München Germany 1. Introduction The results of an automated visual inspection (AVI) system depend strongly on the image acquisition procedure. In particular, the illumination plays a key role for the success of the following image processing steps. The choice of an appropriate illumination is especially cri- tical when imaging 3D textures. In this case, 3D or depth information about a surface can be recovered by combining 2D images generated under varying lighting conditions. For this kind of surfaces, diffuse illumination can lead to a destructive superposition of light and sha- dows resulting in an irreversible loss of topographic information. For this reason, directional illumination is better suited to inspect 3D textures. However, this kind of textures exhibits a different appearance under varying illumination directions. In consequence, the surface in- formation captured in an image can drastically change when the position of the light source varies. The effect of the illumination direction on the image information has been analyzed in several works [Barsky & Petrou (2007); Chantler et al. (2002); Ho et al. (2006)]. The changing appearance of a texture under different illumination directions makes its inspection and clas- sification difficult. However, these appearance changes can be used to improve the knowledge about the texture or, more precisely, about its topographic characteristics. Therefore, series of images generated by varying the direction of the incident light between successive captures can be used for inspecting 3D textured surfaces. The main challenge arising with the varia- ble illumination imaging approach is the fusion of the recorded images needed to extract the relevant information for inspection purposes. This chapter deals with the fusion of image series recorded using variable illumination direc- tion. Next section presents a short overview of related work, which is particularly focused on the well-known technique photometric stereo. As detailed in Section 2, photometric stereo allows to recover the surface albedo and topography from a series of images. However, this method and its extensions present some restrictions, which make them inappropriate for some problems like those discussed later. Section 3 introduces the imaging strategy on which the proposed techniques rely, while Section 4 provides some general information fusion concepts and terminology. Three novel approaches addressing the stated information fusion problem 5 Sensor Fusion and Its Applications92 are described in Section 5. These approaches have been selected to cover a wide spectrum of fusion strategies, which can be divided into model-based, statistical and filter-based me- thods. The performance of each approach are demonstrated with concrete automated visual inspection tasks. Finally, some concluding remarks are presented. 2. Overview of related work The characterization of 3D textures typically involves the reconstruction of the surface topo- graphy or profile. A well-known technique to estimate a surface topography is photometric stereo. This method uses an image series recorded with variable illumination to reconstruct both the surface topography and the albedo [Woodham (1980)]. In its original formulation, under the restricting assumptions of Lambertian reflectance, uniform albedo and known po- sition of distant point light sources, this method aims to determine the surface normal orien- tation and the albedo at each point of the surface. The minimal number of images necessary to recover the topography depends on the assumed surface reflection model. For instance, Lambertian surfaces require at least three images to be reconstructed. Photometric stereo has been extended to other situations, including non-uniform albedo, distributed light sources and non-Lambertian surfaces. Based on photometric stereo, many analysis and classification approaches for 3D textures have been presented [Drbohlav & Chantler (2005); McGunnigle (1998); McGunnigle & Chantler (2000); Penirschke et al. (2002)]. The main drawback of this technique is that the reflectance properties of the surface have to be known or assumed a priori and represented in a so-called reflectance map. Moreover, methods based on reflectance maps assume a surface with consistent reflection characteristics. This is, however, not the case for many surfaces. In fact, if location-dependent reflection properties are expected to be utilized for surface segmentation, methods based on reflectance maps fail [Lindner (2009)]. The reconstruction of an arbitrary surface profile may require demanding computational ef- forts. A dense sampling of the illumination space is also usually required, depending on the assumed reflectance model. In some cases, the estimation of the surface topography is not the goal, e.g., for surface segmentation or defect detection tasks. Thus, reconstructing the surface profile is often neither necessary nor efficient. In these cases, however, an analogous imaging strategy can be considered: the illumination direction is systematically varied with the aim of recording image series containing relevant surface information. The recorded images are then fused in order to extract useful features for a subsequent segmentation or classification step. The difference to photometric stereo and other similar techniques, which estimate the surface normal direction at each point, is that no surface topography reconstruction has to be expli- citly performed. Instead, symbolic results, such as segmentation and classification results, are generated in a more direct way. In [Beyerer & Puente León (2005); Heizmann & Beyerer (2005); Lindner (2009); Pérez Grassi et al. (2008); Puente León (2001; 2002; 2006)] several image fusion approaches are described, which do not rely on an explicit estimation of the surface topogra- phy. It is worth mentioning that photometric stereo is a general technique, while some of the methods described in the cited works are problem-specific. 3. Variable illumination: extending the 2D image space The choice of a suitable illumination configuration is one of the key aspects for the success of any subsequent image processing task. Directional illumination performed by a distant point light source generally yields a higher contrast than multidirectional illumination pat- terns, more specifically, than diffuse lighting. In this sense, a variable directional illumination strategy presents an optimal framework for surface inspection purposes. The imaging system presented in the following is characterized by a fixed camera position with its optical axis parallel to the z-axis of a global Cartesian coordinate system. The camera lens is assumed to perform an orthographic projection. The illumination space is defined as the space of all possible illumination directions, which are completely defined by two angles: the azimuth ϕ and the elevation angle θ; see Fig. 1. Fig. 1. Imaging system with variable illuminant direction. An illumination series S is defined as a set of B images g(x, b b ), where each image shows the same surface part, but under a different illumination direction given by the parameter vector b b = (ϕ b , θ b ) T : S = {g(x, b b ), b = 1, . . . , B}, (1) with x = (x, y) T ∈ R 2 . The illuminant positions selected to generate a series {b b , b = 1, . . . , B} represent a discrete subset of the illumination space. In this sense, the acquisition of an image series can be viewed as the sampling of the illumination space. Beside point light sources, illumination patterns can also be considered to generate illumina- tion series. The term illumination pattern refers here to a superposition of point light sources. One approach described in Section 5 uses sector-shaped patterns to illuminate the surface si- multaneously from all elevation angles in the interval θ ∈ [0 ◦ , 90 ◦ ] given an arbitrary azimuth angle; see Fig. 2. In this case, we refer to a sector series S s = {g(x, ϕ b ), b = 1, . . . , B} as an image series in which only the azimuthal position of the sector-shaped illumination pattern varies. 4. Classification of fusion approaches for image series According to [Dasarathy (1997)] fusion approaches can be categorized in various different ways by taking into account different viewpoints like: application, sensor type and informa- tion hierarchy. From an application perspective we can consider both the application area and its final objective. The most commonly referenced areas are: defense, robotics, medicine and space. According to the final objective, the approaches can be divided into detection, recognition, classification and tracking, among others. From another perspective, the fusion [...]... medicine and space According to the final objective, the approaches can be divided into detection, recognition, classification and tracking, among others From another perspective, the fusion 94 Sensor Fusion and Its Applications Fig 2 Sector-shaped illumination pattern approaches can be classified according to the utilized sensor type into passive, active and a mix of both (passive/active) Additionally, the sensor. .. ul and vl corresq pondingly Each element f lijk (S) of the kernel function is obtained by taking the absolute q q value of the difference between the intensities in the positions ul and vl with the same q In Fig 14, the kernel function for a given group of parameters is illustrated In this figure, the 110 Sensor Fusion and Its Applications Fig 14 Kernel function flijk for a image series with B = 4 (∆ϕ... = ggen (x) =    (4) ggen (x)   (1) ai ( x ) k   ∑   si =   i =1 (4) ai ( x ) k ∑ ai ( x ) · si (17) i =1 Whole images are simply obtained by generating contiguous image patches and then joining them together The segmented defect image is obtained following the thresholding scheme shown in Fig 10 This scheme can be explained as follows: 1 04 Sensor Fusion and Its Applications + abs + abs... too An overview 102 Sensor Fusion and Its Applications and description of different approaches and implementations of ICA algorithms can be found in [Hyvärinen & Oja (2000)] The calculation of an independent component si is achieved by means of the inner product of a row vector wT of the ICA matrix W and an observed vector v: i si = wi , v = m (k) ∑ wi k =1 · v(k) , (13) (k) where wi and v(k) are the... for its acquisition: gmnb = g(x, ϕb ) with ϕb = b ∆ϕ and 0 ≤ b ≤ B −1 (21) Rewriting Eq (20) to consider series of images, we obtain: f˜l (S) = M −1 N −1 K −1 ∑ ∑ ∑ i =0 j =0 k =0 f l (tijk {S}) (22) The transformed series of images tijk {S} can be defined as follows: ˜ tijk {S} =: { gm n b , b = 1, , B} , (23) 108 Sensor Fusion and Its Applications where the vector (m , n )T is the translated and. .. extraction from illumination series is presented in [Nachtigall & Puente León (2009)] Section 5.2 describes an approach based on ICA filters and illumination series which allows a separation of texture and defects The performance of this 96 Sensor Fusion and Its Applications method is demonstrated in Section 5.2.5 with an AVI application: the segmentation of varnish defects on a wood board • Statistical... regions were correctly discerned from the intact background Fig 7 shows a segmentation result based on the model parameters kd (x), kfs (x) and σ(x) This result was obtained by thresholding the three parameter signals, and then combining 100 Sensor Fusion and Its Applications them by a logical conjunction The right image in Fig 7 compares the segmentation result with a manual selection of the worn area... sector-shaped illumination pattern varies 4 Classification of fusion approaches for image series According to [Dasarathy (1997)] fusion approaches can be categorized in various different ways by taking into account different viewpoints like: application, sensor type and information hierarchy From an application perspective we can consider both the application area and its final objective The most commonly... classifier generates a symbolic output (decision level data): the classes of the detected defects 112 Sensor Fusion and Its Applications Rotation Invariant Image series Rotation invariant DAI-FEO Rotation and Translation Invariant Translation invariant FEI-FEO Defect class SVM FEI-DEO DAI-DEO Fig 16 Fusion architecture scheme for the method based on invariant features 6 Conclusions The illumination... have been presented The potentials and benefits of using multi-image analysis methods and their versatility have been demonstrated with a variety of nontrivial and demanding machine vision tasks, including the inspection of varnished wood boards and machined metal pieces such as cutting inserts The fusion of images recorded with variable illumination direction has its roots in the wellknown photometric . while Section 4 provides some general information fusion concepts and terminology. Three novel approaches addressing the stated information fusion problem 5 Sensor Fusion and Its Applications9 2 are. System and Inertial Navigation, McCraw- Hill professional, New York Gelb, A. (19 74) . Applied Optimal Estimation. M. I. T. Press, MA. Sensor Fusion and Its Applications9 0 Grewal, M. S. & Andrews,. Sensor Fusion and Its Applications8 4 INS GPS KF + - measurement prediction )( * xh ATS + + x GPS x INS Determination of P λ and R λ Estimated