G. Adiv. Inherent ambiguities in recovering 3d motion and structures from noisy flow field. IEEE Trans. on PAMI, 11(5):477--489, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....While many solutions to this problem have been proposed, either using feature correspondences or flow fields, they do not work well for real, complex scenes, and most of them degrade ungracefully as the quality of the data deteriorates. Many error analyses have been carried out in the past [1, 5, 7, 19, 23, 24]; a recent illuminating and critical survey is presented in [6] They attempt to model either the errors in the motion estimates or those in the depth estimates, but due to the large number of unknowns in the problem, most of them deal with restricted conditions such as planarity of the scene [1, ....

.... 24] a recent illuminating and critical survey is presented in [6] They attempt to model either the errors in the motion estimates or those in the depth estimates, but due to the large number of unknowns in the problem, most of them deal with restricted conditions such as planarity of the scene [1, 5] or nonbiasedness of the estimators [5, 24] Although these analyses are deep and complex, notably absent in all of them is an account of the systematic nature of the errors in the depth estimates that result from errors in the motion estimates. In other words, the highly correlated nature of the ....

G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:477--489, 1989.

.... number of studies have given rise to three crisp results regarding noise sensitivity in structure from motion [7] These are: a) A translation can be easily confounded with a rotation in the case of a small field of view under the assumption of lateral motion and insufficient variation of depth [1, 6]. Intuitively, translation along the x axis can be confused with rotation around the y axis and translation along the y axis with rotation around the x axis. Evidence for this result can be obtained intuitively from the flow equation (1) As can be seen, if the scene in view is a plane, then the ....

G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:477-- 489, 1989.

....and introduces unnecessary complexity in the sequel. 10 4.3 Finding the focus of expansion The task of finding the translation of an arbitrary affine motion field is quite difficult. For some scene surfaces, there may exist several solutions, as has been shown in various ambiguity studies [1, 15]. Even if the motion field is not ambiguous in theory, a small field of view and measurement errors may prevent us from finding the correct solution in practice. Fortunately, it is much easier to propose an algorithm that works well for real scenes, even though it may not find the right solution ....

G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:477--489, 1989.

....apply the synchronous approach to real time active visual reconstruction. We present the integration of different new techniques for the structure estimation of a robot environment by means of an active vision scheme. Recovering 3D structure from images is one of the main issues in computer vision [1] [7] 9] 19] The approach we have chosen to get an accurate three dimensional geometric description of a scene is based on the active vision paradigm and consists in controlling the motion of a moving camera. The idea of using active schemes to address vision issues has been recently introduced ....

....estimation characterizes a domain of research called dynamic vision. Approaches for 3D structure recovery can be divided into two main classes: the discrete approach, where images are acquired at distant time instants [7] 10] and the continuous approach, where images are considered at video rate [1][9] 19] The method presented here is a continuous approach which stems from the interaction matrix related to the considered primitive. More precisely, we use a structure from controlled motion method which consists in constraining the camera motion in order to obtain a precise and robust ....

G. Adiv. - Inherent ambiguities in recovering 3D motion and structure from a noisy flow field. - IEEE Trans. on PAMI, 11(5):477-489, May 1989.

....of such image patch. Using ego motion as the local measurement is an improvement over using projective homography, since it exploits the ground plane geometry. However, estimating ego motion based on small image patch still suffers from ambiguities among its parameters due to small field of view [2, 7]. To overcome the above difficulty, we exploit the fact that the vehicle motion can be approximated by planar motion on the ground. Such planar motion is of great practice importance and has been used in structure from motion and camera calibration [18, 4] and vehicle ego motion estimation [22] ....

....ill conditioned. There are inherent ambiguities between rotation and translation. Given a small image patch, therefore small field of view (FOV) it is hard to differentiate the wX induced flow from the T Y induced flow, and the w Y induced flow from the TX induced flow, respectively [2, 7]. These inherent ambiguities introduce elongated valley in the SSD error function [3] resulting in slow convergence and bad local minima. It is therefore necessary to exploit the planar motion constraint. To do so, we divide the six ego motion parameters into two triples. The first triple ....

G. Adiv. Inherent ambiguities in recovering 3-d motion and structure from a noisy flow field. PAMI, 11(5), May 1989.

....and the motion of the camera has been a classical problem in Computer Vision for many years. For standard pinhole cameras this is fundamentally a difficult problem. There are strictly ambiguous scenes for which it is impossible to determine all parameters of the motion or the scene structure [1]. There are also effectively ambiguous scenes, for which the structure from motion solution is illconditioned and small errors in image measurements can lead to potentially large errors in estimating the motion parameters [8, 21] These limitations have led to the development of new imaging ....

G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:477--489, 1989.

....problem becomes well posed and stable [7] although still nonlinear. The basic understanding of the influence of the field of view has attracted a few investigators over the years. In this paper we will not study this question in more detail and only refer to the literature for more information [3, 6, 10]. Thus, in conclusion, there are two principles relating camera design to performance in structure from motion the field of view and the linearity of the estimation. These principles are summarized in Fig. 1. A polydioptric spherical camera is therefore the ultimate camera since it combines ....

G. Adiv. Inherent ambiguities in recovering 3D motion and structure from a noisy flow field. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 70--77, 1985.

....is a geometric problem and it exists for both small and large baselines between the views, that is, for the case of continuous motion as well as in the case of discrete displacements of the cameras. The basic understanding of these difficulties has attracted only a few investigators over the years [3, 9, 14, 16]. a) b) Figure 3. Schematic illustration of error function in the space of the direction of translation. a) A valley for a planar surface with a limited field of view. b) A clearly defined minimum for a spherical field of view. Intuitively speaking, for imaging surfaces with small ....

G. Adiv. Inherent ambiguities in recovering 3D motion and structure from a noisy flow field. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 70--77, 1985.

....is a geometric problem and it exists for both small and large baselines between the views, that is, for the case of continuous motion as well as in the case of discrete displacements of the cameras. The basic understanding of these difficulties has attracted only a few investigators over the years [3, 8, 13, 15]. Having in mind the design of an optimal sensor, we are interested in how the stability of the estimation of motion changes with the field of view. In particular, we have compared the planar small field of view camera with a spherical camera [10] Since motion estimation amounts to solving some ....

G. Adiv. Inherent ambiguities in recovering 3D motion and structure from a noisy flow field. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 70--77, 1985.

....is a geometric problem and it exists for both small and large baselines between the views, that is, for the case of continuous motion as well as in the case of discrete displacements of the cameras. The basic understanding of these difficulties has attracted only a few investigators over the years [3, 11, 12, 19, 21]. Having in mind the design of an optimal sensor, we are interested in how the stability of the estimation of motion changes with the field of view. In particular, we have compared the planar small field of view camera with a spherical camera [14] Since motion estimation amounts to solving some ....

G. Adiv. Inherent ambiguities in recovering 3D motion and structure from a noisy flow field. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 70--77, 1985.

....Weng, Huang, and XThis research has been supported by the Defense Advanced Research Projects Agency under RADC contract F30602 87 C 0140 and Army ETL contract DACA76 89 C 0017. Ahuja [8] have given some qualitative conditions for bet ter structure recovery, based primarily on simulations. Adiv [14] has characterized and demonstrated situations where inherent ambiguities exist in the interpretation of noisy flow fields. In addition to the above there are a large number of other serious studies of this problem (see the review in [15] However, what is lacking is a comprehensive ....

....to subpixel precisions; b) f is of the order of hundreds of pixels or less. In this context it should be mentioned that equation 2) suggests that the effect of uncertainties in image splacements on rotational motion parameters can be reduced by having a larger focal length. However it is known [14] that a large field of view is necessary to facil itate the determination of motion parameters. However, for the same image resolution a large field of view means that the focal length is small. Hence it does not seem likely that this problem can be surmounted. 5 Effect of Small Displacement ....

Gilad Adiv. Inherent ambiguities in recovering 3-d mo- tion and structure from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, pages 477-489, May 1989.

....can be solved only by using more visual cues. Generally, the 3 D structure and motion estimation using feature based or intensitybased SFM methods are divided into two steps, i.e. first computing the optical flow of an image sequence and then extracting the structure and motion parameters from it [Adi89]. Various methods about the optical flow estimation are put forward by many researchers. A method in [LB93] can estimate both the optical flow with discontinuities and the related occlusion effectively, where the main error sources of computing the optical flow can be satisfactorily eliminated. ....

G. Adiv,Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field, IEEE Trans. Pattern Anal. Mach. Intelligence, Vol. 11, 1989, pp. 477-489

....on the form of the objective function, the kind of motion, and the geometry of the problem has been seldom investigated thoroughly. Likewise, very few error analyses lead to explicit formulations of the error sensitivity in terms of the input error, the motion and the structure of the scene. Adiv 89] pointed out inherent ambiguities in determining the motion of a planar patch. In particular he discovered that, when the field of view is small, it is impossible to distinguish a pure translational motion parallel to the image plane (v = p 1 ; p 2 ; 0) T ) from a pure rotational motion about ....

....reliably estimated in the presence of noise. The influence on the error sensitivity of the translation direction has been emphasized by [Weng et al. 89b] Horn Weldon 88] by geometric arguments. The importance of the translation direction has been shown experimentally by [Mitiche et al. 87] Adiv 89] and [Weng et al. 89b] Weng et al. 89b] carried out an analysis of the errors in the estimated eigenvectors in order to compare it with the actual error. However, they did not show any explicit dependence of the error on the motion and structure parameters. Weng et al. 89a] recognized the ....

G. Adiv, Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-11 (1989) 477-489.

....carrying out intrinsic nonlinear search schemes. In spite of the thorough understanding of the geometry of the problem practical di#culties of obtaining robust solutions led to numerous studies of local minima and sensitivity in general and or more specific configurations [18, 24] For example, [1, 23, 18] explored rotation and translation confounding from the point of view of noise and the source and presence of local extrema which are intrinsic to the structure from motion problem (i.e. these local extrema are independent of the choice of objective functions) In our study on intrinsic ....

G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(5):477--89, 1989.

....avoid hampering) in a task. Despite the many exciting applications and the energetic progress of research in structure and motion recovery algorithms, many problems remain unsolved. Some of these issues are related to numerical stability and or ambiguity of the solution under general conditions [2, 33, 43, 45, 54, 55]. Other problems stem from the rich variety of shapes and motions that are possible in the world. In particular, many shapes can be non planar and or their motion can be nonrigid. Unfortunately, all of the above mentioned approaches assume that object points in 3D space must remain at fixed ....

G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. PAMI, 11(5), 1989.

....contribution of this section is experimental. We address two questions: 12 . 0.25 0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 0.25 0.25 0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 0. 25 29 31 31 32 16 14 17 14 20 17 20 20 25 25 28 22 31 30 31 32 14 15 14 13 22 19 22 20 22 21 22 21 Error for PUMA with T=[2 3 1] , with 3 local minima at the Depths shown at positions of tracked points in first image. 5 4 3 2 1 0 1 2 3 4 5 5 0 5 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Error for Puma with T= 2 3 1] x y (a) b) Figure 2: Contour and surface plots of the error E T as a function of e, with the ....

....14 17 14 20 17 20 20 25 25 28 22 31 30 31 32 14 15 14 13 22 19 22 20 22 21 22 21 Error for PUMA with T= 2 3 1] with 3 local minima at the Depths shown at positions of tracked points in first image. 5 4 3 2 1 0 1 2 3 4 5 5 0 5 0 0.005 0.01 0.015 0.02 0.025 0.03 0. 035 Error for Puma with T=[2 3 1] x y (a) b) Figure 2: Contour and surface plots of the error E T as a function of e, with the structure derived from the PUMA sequence. The arrows indicate the local gradient direction; red denotes a large error. The error with T = 2; 3; 1) T has 3 forward local minima marked by . Depths ....

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G. Adiv, \Inherent ambiguities in recovering 3-D motion and structure from a noisy ow eld," PAMI 11, 477-489, 1989. 29

.... between points and epipolar lines, and gradientweighted epipolar errors [33] or epipolar improvement [31] 3 relief ambiguity, in general, can characterized as the most sensitive direction in which the rotation and translation estimates are prone to be confound with each other (for example, see [1, 31, 22] for a more detailed analysis) Here we apply the same line of thought to the discrete case. Since the bas relief effect is evident only when the field of view and the depth variation of the scene are small, we here are more interested in characterizing, besides the bas relief ambiguity, other ....

G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(5):477--89, 1989.

....an error analysis needs to be performed. The problem of determining the epipolar geometry of a stereo rig is also known as the structure from motion problem in the motion analysis literature. A significant research effort has been devoted to the analysis of errors in structure from motion, e.g. [1, 18, 17, 52, 19, 31, 20], to cite just a few examples. One common characteristic of these approaches is that their error models are linear. The main reason for this is the mathematical and computational tractability of the linear model. A secondary reason is the lack of an adequate non linear error model. In this ....

G. Adiv. Inherent ambiguities in recovering 3D motion and structure from a noisy flow field. IEEE Trans. Pattern Analysis and Machine Intelligence, 11:477--489, 1989.

....depth minimization from normal flow, given a rotational error the obtained solution will have no error in the translation. In other cases ambiguities remain. In the spherical eye case the analysis is simply performed for noiseless flow. A large number of error analyses have been carried out [2, 12, 13, 15, 29, 41, 43, 44] in the past for a camera type eye, while there is no published research of this kind for the full field of view case. None of the existing studies, however, has attempted a topographic characterization of the function to be minimized for the purpose of analyzing different motion techniques. All ....

G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:477--489, 1989.

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G. Adiv. Inherent ambiguities in recovering 3d motion and structures from noisy flow field. IEEE Trans. on PAMI, 11(5):477--489, 1989.

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G. Adiv. Inherent ambiguities in recovering 3D motion and structure from a noisy flow field. IEEE Trans. on Pattern Analysis and Machine Intelligence, 11:477--489, May 1989.

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G. Adiv. Inherent ambiguities in recovering 3d motion and structure from a noisy flow field. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 70 -- 77, 1985. 24

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G. Adiv. Inherent ambiguities in recovering 3-D motion and structures from noisy flow field. IEEE Trans. on PAMI, 11(5):477--489, 1989.

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G. Adiv. Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field. IEEE Trans. PAMI, 11(5):477--489, 1989.

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Gilad Adiv. Inherent ambiguities in recovering 3-d motion and structure from noisy flow field. IEEE Trans on PAMI, Vol. 11(5):477, May 1989.

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