G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7(4):384--401, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....January 19, 1999 1 Introduction The goal of computer vision algorithms is to extract geometric, photometric and semantic information from image data. This may include the position and identity of an object [2, 8, 20, 38, 49, 59] the motion of a camera attached to a car or an autonomous vehicle [1, 6, 18], the geometry of object surfaces [10, 14, 71] or the transformations necessary to build a large composite image (a mosaic) from a series of overlapping images of the same scene [36, 70] The processes used to extract this information each require some form of parameter estimation to describe ....

....and therefore the pixels of a given image I m to a reference image I r which will form the center of the mosaic. Most mosaic construction techniques in computer vision formulate T as an affine transformation in two dimensions [6] or as the model of the apparent (image) motion of a planar surface [1]. These yield 6 parameter and 8 parameter transformation models, respectively. Unfortunately, these models yield substantial mapping errors for the curved surface of the retina. As a result, a 12 parameter transformation model is required, which models the motion of a quadratic surface imaged ....

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G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7(4):384--401, 1985.

....Spatial grouping allows a significant reduction of complexity, since points need not be detected and tracked individually. 1. 1 Relation to previous work The present work falls within the category of structure from motion, a field that encompasses a vast variety of research efforts, such as [1, 3, 5, 9, 10, 12, 14, 15, 16, 18, 19, 21, 22, 23, 24, 25, 28, 29, 31]. Of all the work in SFM, we consider in particular causal estimation algorithms. A batch approach would obviously perform better, but at the expense of compromising the usability for control actions such as manipulation, navigation or, more in general, real time interaction. Since we integrate ....

....to the measurement equation. As all these techniques are equivalent from a theoretical point of view, we will not make any choice here. Also, for ease of notation, we will write the normals in the state with all three components. We choose as initial conditions # 0 = 1, # 0 = 0, # 0 = [ 0 0 1 ] , T 0 = 0,# 0 = 0, V 0 = 0, # 0 = 0, i = 1, 2 . K. For the initial variance P 0 , choose it to be zeros for # , a large positive number M for each component of # , and zeros corresponding to T and# (note that this has effectively fixed the inertial reference frame to coincide ....

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G. Adiv, Determining 3-d motion and structure from optical flow generated by several moving objects, IEEE Trans. Pattern Analysis and Machine Intelligence 7, no. 4, 384--401, July 1985.

.... Numerous methods have been developed for motion recovery from image sequences, among them are algorithms that compute the motion directly from the grey level values or local measures of them [14, 20, 16, 3, 17] A second class of algorithms use feature points or optical flow to recover motion [1, 9, 15]. A probabilistic error minimization algorithm [26] can be used to recover motion in the presence of outliers. Another class of algorithms use explicit probability distributions of the motion vectors to calculate motion models [23] Black and Anandan presented [7] a framework for robust ....

G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Trans. on Pattern Analysis and Machine Intelligence, 7(4):384--401, July 1985.

....only recover the direction of the camera translation. Without loss of generality, we set d = in our experiments. 2. 2 Direct estimation of ego motion As has been pointed out in [22] in typical traffic scenarios, direct method [11, 8, 6, 17] is more preferable than optical flow based approach [1, 10, 23, 21] for ego motion estimation. The reason is that the road usually has weak texture or linear image structure, while the cluttered background including moving objects often contains many feature points. Given calibrated camera and ground plane normal, we use direct method to estimate the incremental ....

G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. PAMI, 7(4):384-- 401, July 1985.

....entities for content based video access [2] and form the basis for the creation of hypervideo documents [7] They can further be used in object oriented video coding schemes [8] or as initialization for object tracking procedures. Several methods for motion segmentation have been proposed [1, 6, 4, 3]. Most techniques oversegment the frame into a large number of regions and then merge them using some criteria. Criteria for merging are based on measures indicating whether regions move in similar way. The simplest method proposed in [6] uses a scaled euclidean distance. This measure is sensitive ....

....estimation as well as the choice of the scaling matrix. Furthermore, it can be shown that the merging results depend on the choice of the origin of the coordinate system [5] Other methods try to use both estimated motion parameters and residuals between model and data to decide on merging [4, 8, 1]. Due to lack of a rigorous foundation their similarity measures are still ad hoc and have drawbacks. Recently, 3] proposed a merging procedure so that the residual sum of squares over all regions is minimized. Since the algorithm finds a local minimum only, merging results heavily depend on the ....

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G. Adiv. Determining 3d motion and structure from optical flows generated by several moving objects. IEEE Trans. on PAMI, 7(4):384--401, 1985.

....computation or structure and motion estimation. A model based multi window approach is presented in this section. If suppose surfaces of the 3D scene consist of planar patches, considering the planarity and Equation 6, the motion flow field can be expressed using the eight parameter motion model [1, 4]: u(x; y) a 1 x 2 a 2 xy a 3 x a 4 y a 5 v(x; y) a 1 xy a 2 y 2 a 6 x a 7 y a 8 : 8) By substituting u(x; y) and v(x; y) of Equation 8 into Equation 5, one can get G(x; y) T A = 0; 9) where G(x;y) 2 6 6 6 6 6 4 Exx 2 Eyxy 3Ex Exxy Eyy 2 3Ey ....

G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. PAMI, 7(4):384-- 401, July 1985.

....from motion (SFM) algorithms. In fact, any SFM algorithm can be used as a starting point. As such, it relates to a vast portion of the literature of Computational Vision that cannot be reviewed within the space allotted. A few references that we find to be most closely related to our approach are [1, 3, 4, 5, 11, 7, 8, 12, 10, 13, 16, 29, 19, 20, 21, 23, 22, 26, 30] but the list is by no means complete. The reader can refer to new and upcoming textbooks for more detailed references on general SFM. Since we integrate tracking and motion estimation, our work also relates to the large literature on image (2D) motion. However, most tracking schemes rely on point ....

G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Trans. Pattern Analysis and Machine Intelligence, 7(4):384--401, July 1985. 7

....detected and tracked individually. As we discuss in the next section, we are certainly not the first to traverse this path. 1. 2 Relation to previous work The present work falls within the category of structure from motion (SFM) a field that encompasses a vast variety of research efforts, such as [2, 4, 5, 9, 10, 14, 16, 13, 18, 21, 41, 26, 27, 29, 33, 34, 17, 30, 31, 32, 38, 42, 43, 45, 7, 15, 8]. Of all the work in SFM, we consider in particular causal estimation algorithms. A batch approach would obviously perform better, but at the expense of making the estimates useless when it comes to performing control actions such as manipulation, navigation or, more in general, real time ....

G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Trans. Pattern Analysis and Machine Intelligence, 7(4):384--401, July 1985.

....(camera tracking) have a long history in computer vision (e.g. Gennery 82; Lowe 92; Gennery 92; Zhang Faugeras 92] Constrained 3D motion estimation is being applied in various robotics and navigation tasks. Much research has been devoted to estimating 3D motion from optical flow fields (e.g. Adiv 85] as well as from discrete moving image features like corners or line segments (e.g. Huang 86; Broida et al. 90; Zhang 95] often coupled with structure from motion estimation, or using more than two frames (e.g. Shariat Price 90] The theoretical problems seem to be well understood, but ....

G. Adiv, Determining 3-D motion and structure from optical flow generated by several moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-7, 1985, pp. 384-- 401.

.... Numerous methods have been developed for motion recovery from image sequences; among them are algorithms that compute the motion directly from the grey level values or local measures of them [3, 14, 16, 17, 20] A second class of algorithms use feature points or optical flow to recover motion [1, 9, 15]. A probabilistic error minimization algorithm [26] can be used to recover motion in the presence of outliers. Another class of algorithms use explicit probability distributions of the motion vectors to calculate motion models [23] Black and Anandan presented [7] a framework for robust ....

G. Adiv, Determining 3-d motion and structure from optical flow generated by several moving objects, IEEE Trans. Pattern Anal. Mach. Intell. 7(4), 1985, 384--401.

....# u v # # = x p (u) L p (u) q (2.14) The model based optical flow constraint equation in the image can be found by rewriting (2.13) using (2.14) IL p (u) q I t = 0 (2.15) Formulations which are basically identical to (2. 15) although are often confined to rigid motion) can be found in [Adi85, BAHH92, CAHT94, HW88, LRF93, NH87, NS85] Negahdaripour and Horn [NH87] refers to a formulation such as this as a direct method for motion estimation. The discussion of (2.15) in [BAHH92, NH87, NS85] is specialized for rigid motion, and while still general, requires a lengthy derivation by hand. ....

G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Pattern Analysis and Machine Intelligence, 7(4):384--401, July 1985.

....be quite difficult, however, especially as the deviation between the model and data becomes large. Model based optical flow: Instead of computing an unconstrained flow field (a grid of arrows) a model based approach explains the optical flow information in terms of motion parameters of the model [1, 5, 9, 23, 28, 35, 36]. While the problem is non linear, these frameworks can use either a single step linear least squares solution [9, 28, 36] or an iterative least squares solution [1, 5, 23, 35] The motion model can be a 2D model of image motion [5, 6] or a 3D model (rigid or non rigid) of object motion [5, 9, ....

.... a model based approach explains the optical flow information in terms of motion parameters of the model [1, 5, 9, 23, 28, 35, 36] While the problem is non linear, these frameworks can use either a single step linear least squares solution [9, 28, 36] or an iterative least squares solution [1, 5, 23, 35]. The motion model can be a 2D model of image motion [5, 6] or a 3D model (rigid or non rigid) of object motion [5, 9, 28] along with a camera model to relate to the images) It is also possible to compute an unconstrained optical flow field using standard techniques, and fit a parametric motion ....

[Article contains additional citation context not shown here]

G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Pattern Analysis and Machine Intelligence, 7(4):384--401, July 1985.

....(camera tracking) have a long history in computer vision (e.g. Gennery 82; Lowe 92; Gennery 92; Zhang Faugeras 92] Constrained 3D motion estimation is being applied in various robotics and navigation tasks. Much research has been devoted to estimating 3D motion from optical flow fields (e.g. Adiv 85] as well as from discrete moving image features like corners or line segments (e.g. Huang 86; Broida et al. 90; Zhang 95] often coupled with structure from motion estimation, or using more than two frames (e.g. Shariat Price 90] The theoretical problems seem to be well understood, but ....

G. Adiv, Determining 3-D motion and structure from optical flow generated by several moving objects. IEEE Transactions on

....in representing epipolar deviation and using different techniques to seek the optimization of the resulting functions. Furthermore, there exist techniques that first estimate rotation and, on the basis of the result subsequently estimate translation [9, 37, 38] techniques that do the opposite [1, 23, 26, 31, 33, 39, 42]; and techniques that estimate all motion parameters simultaneously [7, 8, 17, 36, 45] The positive depth constraint, which has been used for normal flow fields, is relatively new and is employed in the so called direct algorithms [8, 21, 27] One has to search for the 3D motion that is ....

G. Adiv. Determining 3D motion and structure from optical flow generated by several moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7:384--401, 1985.

....Algorithms for this problem of 3D interpretation from monocular motion can be broadly divided into two categories two frame and multi frame. Two frame algorithms first compute the relative orientation the translation and rotation between the camera positions at two time instants [1, 12, 14, 29]. Then the relative orientation is used to compute the 3D location for each imaged feature. In addition to advantages and disadvantages specific to instances of these algorithms, the two frame methods suffer from two major problems. First, for some motions, there are inherent ambiguities in the ....

....from Shariat s [25] calculations because we do not assume constant rotational speed or uniform sampling. 9 eigenvalues of a matrix are invariant to rotations of the coordinate system. With 2 = 1 d 2 Gamma k 2 , M exp ] represented in a rotated coordinate system where b and c are [ 0 0 1 ] and [ 0 1 0 ] respectively, has the three eigenvalues: 1 = d 2 2 = 1 2 ( 2 q 2 2 4d 2 k 2 ) 9) 3 = 1 2 ( 2 Gamma q 2 2 4d 2 k 2 ) 10) 1 and 2 have the same sign which is different from that of 3 , except in the degenerate case when d is zero, corresponding to ....

[Article contains additional citation context not shown here]

G. Adiv. Determining 3D motion and structure from optical flows generated by several moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7(4):384--401, 1985.

....of the motion rotation about the camera s optical axis in particular will be small. This generality suggests that the curved nature of the retina surface should be taken into account in the inter image transformation model and that transformation models based on a planar surface [1, 6] will be insufficient. We confirm these intuitions by deriving a Figure 3: Examples showing visually the transformation error obtained using a 0th order image translation only model (left) the affine model (center) and the quadratic model (right) transformation model for a quadratic ....

G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Trans. on PAMI, 7(4):384--401, 1985.

....methods. In image based methods, the displacement of coherent structures is determined on a pixel to pixel basis. Examples of image based techniques are (from image processing) the maximization of the cross correlation between two images [8] and methods (from computer vision) using optical flow [1]. Since these methods involve an optimization process using the original data, they are suitable for 2D images, but are inefficient for 3D fields. In feature based methods, first feature extraction takes place for each frame. The resulting features are then matched to the features in subsequent ....

G. Adiv. Determining 3D Motion and Structure from Optical Flows Generated by several Moving Objects. IEEE Trans. on PAMI, 7:384--401, 1985.

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G. Adiv. Determining 3-d motion and structure from optical flow generated by several moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7(4):384--401, 1985.

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G. Adiv. Determining 3D motion and structure from optical flow generated by several moving objects. IEEE Trans. Pattern Anal. Machine Intell., 7(4):384--401, July 1985.

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G. Adiv. Determining 3d motion and structure from optical flows generated by several moving objects. IEEE Trans. on PAMI, 7(4):384--401, 1985.

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G. Adiv. Determining 3d motion and structure from optical flow generated by several moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7:384 -- 401, 1985.

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G. Adiv, Determining 3-D motion and structure from optical flow generated by several moving objects. IEEE Transactions on

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G. Adiv. Determining 3D Motion and Structure from Optical Flows Generated by several Moving Objects. IEEE Trans. on PAMI, 7:384--401, 1985.

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G. Adiv, Determining 3-D motion and structure from optical flow generated by several moving objects, IEEE Trans. Pattern Analysis and Machine Intelligence PAMI-7 (1985) 384--401.

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G. Adiv. Determining 3D Motion and Structure from Optical Flows Generated by several Moving Objects. IEEE Trans. on PAMI, 7:384#401, 1985.

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