J.M. Dinten. Tomographic reconstruction of axially symmetric objects: Regularization by a markovian modelization. In International Conference on Pattern Recognition, volume 2, pages 153--158, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... be determined directly from the projections [83, 71, 38, 73, 82, 117, 72, 34] or the 3D symmetric object can be reconstructed from its projection and 3D symmetry determined [53, 97, 114, 106, 70, 33] Additional approaches to detection of 3D symmetry involve deformable contours [99] tomography [27], structure from motion techniques [80, 67, 88] and physical mirrors [74, 51, 1, 54] In most of the above mentioned techniques, symmetry is treated as a binary feature: either it exists or it does not exist in an object. The notion of quantifying symmetry has been seldomly discussed; The early ....

....of 3D reconstruction methods from 2D projections is that of computerized tomography. These methods assume the 2D projection represents density of the object along the lines of projection. Classic tomography requires infinite projections to fully reconstruct the object. However, it is shown in [27] that symmetry of the 3D object can be exploited to assist in reconstruction. Specifically, a surface of revolution having axial symmetry, is reconstructed from a single 2D projection in the direction perpendicular to the axis of rotation of the object. Baysean regularization is incorporated into ....

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J.M. Dinten. Tomographic reconstruction of axially symmetric objects: Regularization by a markovian modelization. In International Conference on Pattern Recognition, volume 2, pages 153--158, 1990.

.... the global minimum, and such probabilistic relaxation schemes have raised consider able attention since [2] Unfortunately, SA is numerically intractable in our context (Section 2) This is the main reason why compound MRFs have only been used in restricted situations in similar contexts [3] 4] In order to calculate a weak membrane MAP solu tion, we focus on a deterministic relaxation approach Graduated Non Convexity (GNC) initially developed by Blake Zisserman for the purpose of image segmentation and noise cancellation [1] Section 3) It generally finds nearly optimal minimum, ....

....initially developed by Blake Zisserman for the purpose of image segmentation and noise cancellation [1] Section 3) It generally finds nearly optimal minimum, and at least it avoids the many shallow local minima. However its generalization to inverse problems is not straightforward. In Section 4 we propose a modified GNC optimisation technique that manages any linear ill conditioned observation operator. For a non linear estimator, invariance of the solution from the observation scale is not trivialy satisfied: we present the conditions for the scale invariance of the weak membrane ....

[Article contains additional citation context not shown here]

Dinten J.-M., "Tomographic reconstruction of axially symmetric objects: regularlzatlon by a Markovtan modelisation, " Proc. of the Int. Conf. on Pattern Recog., pp. 153- 158, 1990.

.... the global minimum, and such probabilistic relaxation schemes have raised consider able attention since [2] Unfortunately, SA is numerically intractable in our context (Section 2) This is the main reason why compound MRFs have only been used in restricted situations in similar contexts [3] 4] In order to calculate a weak membrane MAP solu tion, we focus on a deterministic relaxation approach Graduated Non Convexity (GNO) initially developed by Blake Zisserman for the purpose of image segmentation and noise cancellation [1] Section 3) It generally finds nearly optimal ....

....developed by Blake Zisserman for the purpose of image segmentation and noise cancellation [1] Section 3) It generally finds nearly optimal minimum, and at least it avoids the many shallow local minima. However its generalization to inverse problems is not straightforward. In Section 4 we propose a modified GNC optimisation technique that manages any linear ill conditioned observation operator. For a non linear estimator, invariance of the solution from the observation scale is not trivialy satisfied: we present the conditions for the scale invariance of the weak membrane ....

[Article contains additional citation context not shown here]

Dinten J.-M., "Tomographic reconstruction of axially sym- metric objects: regularlzatlon by a Ma-kovian modelisation, " Proc. of the Int. Conf. on Pattern Recog., pp. 153- 158, 1990.

....[18] 25] Such a situation arises in image segmentation, where is diagonal, or in deconvolution problems, when the blur spreads over a small window. However, general forms of SA are intractable under (A1) and (A2) 19] 39] and coupled MRF s have been used only in several special cases. In [12], an MRF with a label field is used for the reconstruction of objects with axial symmetry from X ray tomography data. In this case supp is moderate (supp is a line going through object ) and a local minimum is calculated using the iterated conditional modes (ICM) algorithm. Recently, an ....

J.-M. Dinten, "Tomographic reconstruction of axially symmetric objects: Regularization by a Markovian modelization," in Proc. Int. Conf. on Pattern Recognition, 1990.

....pixels. Projections are then based on strip band integration of , see [10] for example. Assume we model the scene by a set of binary cubic voxels # ) where each voxel value is equal to 1 if the centre of the voxel is inside the fault, and 0 otherwise [11, 1]. Operator becomes linear towards and equation (2) rereads , 3) where , stands for the X ray projection matrix, whose elements are the length of the intersections between each voxel and each projection line. In case of contour reconstruction, the scene is described by the ....

J.-M. Dinten, "Tomographic reconstruction of axially symmetric objects: Regularization by a Markovian modelisation," in Proc. of the Int. Conf. on Pattern Recog., 1990.

....restriction of a MRF, subsampling. I. Introduction M ARKOV Random Field (MRF) models have been successfully introduced in many fundamental issues of image analysis and computer vision such as image restoration [5] 14] edge detection [13] image segmentation [9] 13] computed tomography [11], surface reconstruction [9] 30] stereovision [2] motion analysis [18] 24] 37] or scene interpretation [33] The mathematical framework is a statistical one: entities of interest in a given task are described by statistical models (Markov random fields) and Bayesian estimation theory is used ....

J.-M. Dinten, "Tomographic reconstruction of axially symmetric objects: regularization by a Markovian modelization," In Proc. Int. Conf. Pattern Recognition, vol.2, pp. 153-158, Atlantic City, 1990.

....detector pixels. Projections are then based on strip band integration of f(x) see [10] for example. Assume we model the scene S by a set of n binary cubic voxels f = f 1 ; f n ] t , where each voxel value is equal to 1 if the centre of the voxel is inside the fault, and 0 otherwise [11, 1]. Operator A becomes linear towards f and equation (2) rereads d = Af n; 3) where A stands for the X ray projection matrix, whose elements are the length of the intersections between each voxel and each projection line. In case of contour reconstruction, the scene is described by the contour C ....

J.-M. Dinten, "Tomographic reconstruction of axially symmetric objects: Regularization by a Markovian modelisation," in Proc. of the Int. Conf. on Pattern Recog., 1990.

....algorithms [18, 25] Such a situation arises in image segmentation, where A is diagonal, or in deconvolution problems, when the blur spreads over a small window. However, general forms of SA are intractable under (A1,A2) 39, 19] and coupled MRFs have been used only in several special cases. In [12], a MRF with a label field is used for the reconstruction of objects with axial symmetry from X ray tomography data. In this case supp (A T A) is moderate (supp a j is a line going through object x) and a local minimum is calculated using the iterated conditional modes (ICM) algorithm. ....

J.-M. Dinten, "Tomographic reconstruction of axially symmetric objects: regularization by a Markovian modelisation", in Proc. of the Int. Conf. on Pattern Recog., 1990.

.... 3 1 Introduction Markov Random Fields (MRF) models have been successfully introduced in many fundamental issues of image analysis and computer vision such as image restoration, 5, 11, 19] edge detection, 18] image segmentation, 13, 18] multisource image analysis, 24] computed tomography, [17], surface reconstruction, 13, 36] stereovision [2] motion analysis [9, 10, 23, 40] or scene interpretation, 37] The mathematical framework is a statistical one: entities of interest in a given task are described by statistical models (Markov Random Fields) and bayesian estimation theory is ....

J.M. DINTEN. -- Tomographic reconstruction of axially symmetric objects : Regularization by a markovian modelization. -- In Proc. 10th Int. Conf. Pattern Recognition, volume 2, pages 153--158, Atlantic City, Juin 1990.

.... [24] Symmetrical descriptions of shapes [9, 11, 15, 21] or detection of symmetrical features of objects [34] can be useful in guiding shape matching, model based object matching and object recognition [31, 33] Reconstruction of 3D objects has also been implemented using symmetry as a constraint [36, 14, 29]. More recently, symmetry has been used to discriminate textures [10] and has been used in guiding robot grasping [8] Transformation of the symmetry detection problem to a pattern matching problem introduces efficient algorithms for detection of mirror and rotational symmetries and location of ....

J.M. Dinten. Tomographic reconstruction of axially symmetric objects: Regularization by a markovian modelization. In International Conference on Pattern Recognition, volume 2, pages 153--158, 1990.

.... Graph 3 1 Introduction Markov Random Fields (MRF) models have been successfully introduced in many fundamental issues of image analysis and computer vision such as image restoration [5, 11, 19] edge detection [18] image segmentation [13, 18] multisource image analysis [24] computed tomography [17], surface reconstruction [13, 36] stereovision [2] motion analysis [9, 10, 23, 40] or scene interpretation [37] The mathematical framework is a statistical one: entities of interest in a given task are described by statistical models (Markov Random Fields) and Bayesian estimation theory is used ....

J.M. DINTEN. -- Tomographic reconstruction of axially symmetric objects : Regularization by a Markovian modelization. -- In Proc. 10th Int. Conf. Pattern Recognition, volume 2, pages 153--158, Atlantic City, Juin 1990.

....restriction of a MRF, subsampling. I. Introduction M ARKOV Random Field (MRF) models have been successfully introduced in many fundamental issues of image analysis and computer vision such as image restoration [5] 14] edge detection [13] image segmentation [9] 13] computed tomography [11], surface reconstruction [9] 30] stereovision [2] motion analysis [18] 24] 37] or scene interpretation [33] The mathematical framework is a statistical one: entities of interest in a given task are described by statistical models (Markov random fields) and Bayesian estimation theory is used ....

J.-M. Dinten, "Tomographic reconstruction of axially symmetric objects: regularization by a Markovian modelization," In Proc. Int. Conf. Pattern Recognition, vol.2, pp. 153-158, Atlantic City, 1990.

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