Denis N. Lee. The optic flow field: The foundation of vision. Philosophical Transactions of the Royal Society of London, Series B, B290:169--179, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Such a time to collision r( is very simple to derive for a mobile robot. It equals the time along the camera curve to reach the point: r(r ) sin (Z(x Y)n) 14) which can be calculated by a parameterization of (9) to time. Notice that this time to collision does not equal the usual definition [13] of the depth divided by the translational velocity; we have considered circular motion, not rectlinear motion 8 Experiments The approach, described in previous sections, is tested with a set of calibrated image sequences. We obtained an accurate motion of the camera by mounting the camera in ....

D.N. Lee. The optic flow field: the foundation of vision. Philosophical Transactions of the Royal Society of London, vol. B, 290, pp169-179, 1980.

....illustrating collision detection and obstacle avoidance have been developed. 1 1 Introduction Any mobile active vision system [1, 2] should have the capability to safeguard itself against accidental collision with surrounding objects, both due to its own motion and the motion of other objects [3, 4, 5, 6, 7, 8]. In this paper we describe the design and implementation of a real time system for collision detection based on computer vision. The system consists of a video camera mounted on a mobile robot. The camera grabs images at the rate of 25 frames sec (25 Hz) and feeds them to a vision engine. The ....

D.N.Lee. The optic flow field: the foundations of vision. Phil. Trans. R. Soc. London, 290, 1980.

.... OE (x) R d f(x )OE( 9 one s task, a 0 th order approximation is usually too restrictive. For example, in the case of real world movies, 1 st order properties of the vector field may reveal relevant information such as qualitative shape properties, surface slant [47] and time to collision [51, 52]. Unlike 1 st order, 2 nd order is quantitatively related to intrinsic surface properties of an object [50] There is no a priori limit to the highest order that is still accessible and significant; this depends very much on matters such as image quality (noise and sampling characteristics) ....

D. N. Lee. The optic flow field: the foundation of vision. Phil. Trans. R. Soc. Lond. B, 290:169--179, 1980.

.... ( r) is very simple to derive for a mobile robot. It equals the time along the camera curve to reach the point: r) sin Gamma1 (Z(x; y) Omega y (14) which can be calculated by a parameterization of (9) to time. Notice that this time to collision does not equal the usual definition [13] of the depth divided by the translational velocity; we have considered circular motion, not rectlinear motion 8 Experiments The approach, described in previous sections, is tested with a set of calibrated image sequences. We obtained an accurate motion of the camera by mounting the camera in the ....

D.N. Lee. The optic flow field: the foundation of vision. Philosophical Transactions of the Royal Society of London, vol. B, 290, pp169-179, 1980.

....quantities are expressed in time , where we define = 0 as the moment of contact between the end effector and object. Therefore, increasing t means decreasing , as long as the object and camera are approaching. Is known as the time to contact and has been shown to have biological relevance [11]. We will first assume that the camera moves towards the object with a constant acceleration a( in Cartesian domain. The vertical distance d( between the object and the end effector then is d(0) d( v( 1 2 a( 2 ; 3a) v(0) v( a( 3b) where v( is the velocity with ....

....e( 5a) a( v( e( e( Gamma 3 2 e( e( 5b) The values of d( v( and a( v( are the measurable quantities of the system which can be obtained from sensor information only. In particular, if a( 0 from that moment onwards then d( v( equals time to contact [11]. Also, in that case we have that t is constant. A. Deceleration in visual domain Perfect deceleration means that the robot moves to the state where the distance between the target object and the gripper (c.q. camera) is zero, and the robot is in rest. The deceleration criterion can thus be ....

D. N. Lee, "The optic flow field: The foundation of vision," Phil. Trans. R. Soc. Lond. B 290 (1980), 169--179.

....time is known as the time to contact and indicated by the symbol . When the system is not accelerating, is given by the quotient of the distance from an approaching surface and the velocity toward it. Exactly the same information can be obtained from the divergence of the approaching surface [4,5] a feature that can be observed monocularly. 2 Since this bird cannot measure its velocity, it measures the time until it hits the water from the time derivatives of visual observation. It is this mechanism that underlies the method presented in this chapter for controlling a monocular robot ....

....decelerate toward an object, by having it satisfy the constraint on those quantities. Note that the time until contact cannot be controlled; it is, in fact, equal to 2a 0 =a 1 and thus depends on the initial position and velocity of the system only. This case has been investigated by Lee [5]. 0. Preface 45 Cubic Polynomials As mentioned above, for n 2, no solutions exist in the general case. As an example, for n = 3, 3.7) reduces to the combined equations n = 3 : a 3 2 a 0 a 2 3 = 1 27 ; a 3 a 1 a 2 2 = 1 3 : 3.10) This set of equations leads to two, possibly ....

D. N. Lee. The optic flow field: the foundation of vision. Phil. Trans. R. Soc. Lond. B, 290:169--179, 1980.

....y) is very simple to derive for a mobile robot. It equals the time along the camera curve to reach the point: x; y) sin Gamma1 (Z(x; y) Omega y (10) which can be calculated by a parameterization of (5) to time. Notice that this time to collision does not equal the usual definition [14] of the depth divided by the translational velocity; we have considered circular motion, not rectlinear motion 5 Experiments We carried out an experiment to test the accuracy of the prediction of collision points. We used a 1 3 black white CCD camera for which we computed the collision ....

D.N. Lee. The optic flow field: the foundation of vision. Philosophical Transactions of the Royal Society of London, vol. B, 290, pp169-179, 1980.

....impose a second constraint on the control system: while tracking a target, we want the system to maintain a constant distance away from the target. Such a task requires more complex visual information processing. In particular, we compute from the images the time to collision, or time to contact [25], from the observer to the target, and we use it in the control of the robot. We will now discuss the estimation of time to contact from images; we will also discuss related work and describe the technique used here. Let us note here that traditional methods by which this is accomplished cannot be ....

D.N. Lee, The optic flow field: The foundation of vision. Phil. Trans. Royal Society London, 290, 1980.

....and indicated by the symbol . When the system is not accelerating, is given by the quotient of the distance from an approaching surface and the velocity towards it. Exactly the same information can be obtained from the divergence of the approaching surface (Koenderink Doorn, 1975; Lee, 1980) a feature that can be observed monocularly. Since this bird cannot measure its velocity, it measures the time until it hits the water from time derivatives of the visual observation. It is this mechanism that underlies the method presented in this paper for controlling a monocular robot arm ....

Lee, D. N. (1980). The optic flow field: the foundation of vision. Phil. Trans. R. Soc.

....thus, mobile robotics provides a promising test bed for ecological principles. Optical Flow and Control Laws A relevant case is the study of optical flow. As an observation point moves through the environment, the pattern of light reflected to that point changes continuously, creating optical flow (Lee, 1980; Gibson, 1958) Optical flow contains information about both the layout of surfaces and the motion of the point of observation. For example, if an observer is translating, the focus of expansion (FOE) or center of the radial flow pattern, specifies the observer s heading. If the observer is ....

Lee, D.N. (1980). The optic flow field: The foundation of vision. Phil. Trans. R. Soc. of Lond. B, 290, 169-179.

....position and orientation and that this partial solution can be used to perform useful visual tasks when augmented with additional information. Useful applications include providing information which is used by pilots when landing aircraft [15] estimating time to contact in braking reactions [28] and in the recovery of 3D shape up to a 3D affine (relief) transformation [26, 27] We now show how surface orientation and position (expressed as a time to contact) can be recovered from the estimates of image divergence and the magnitude and axis of the deformation component. 1. With knowledge ....

....linear, as predicted. These results are of useful accuracy, predicting the collision time to the nearest half time unit (corresponding to 50cm in this example) For non uniform motion the profile of the time to contact as a function of time is a very important cue for braking and landing reactions [28]. 5.2.2 Collision avoidance It is well known that image divergence can be used in obstacle collision avoidance. Nelson and Aloimonos [32] demonstrated a robotics system which computed divergence by spatio temporal techniques applied to the images of highly textured visible surfaces. We describe ....

D.N. Lee. The optic flow field: the foundation of vision. Phil. Trans. R. Soc. Lond., 290, 1980.

....= 2 e(t) e(t) a(t) v(t) e(t) e(t) Gamma 3 2 e(t) e(t) 3) In particular, the expression d(t) v(t) expresses the time left before the camera and observed object collide, provided that the acceleration a = 0. This expression is also called time to contact, usually indicated by c (t) [8]. 3.1 Amount of deceleration Suppose that at time t a constant acceleration a 0 is applied to the system. If the camera must land gracefully on the object, i.e. d(t t ) v(t t ) 0 at some time t t , the desired acceleration a d (t) can be determined from: v(t) Gammaa d (t) Delta (t t ....

....can be determined from: v(t) Gammaa d (t) Delta (t t Gamma t) d(t) v(t) t t Gamma t) 1 2 a d (t) Delta (t t Gamma t) 2 = 1 2 v(t) t t Gamma t) 4) such that Gammav(t) a d (t) 2 d(t) v(t) 5) This relation can also be expressed in image features using eqs. 3) cf. [8]) 3 2 e(t) e(t) Gamma e(t) e(t) Gamma1 = 4 e(t) e(t) or e(t)e(t) e(t) 2 = 5 4 : 6) With eqs. 5) and (3) the desired acceleration a d (t) can be expressed as a function of the current acceleration and the image features: a(t) a d (t) 6 Gamma 4 e(t)e(t) e(t) 2 ....

D. N. Lee, `The optic flow field: The foundation of vision,' Phil. Trans. R. Soc. Lond. B 290 (1980), 169--179.

....to, but not directly towards the nadir. This example also suggests that the viewer is lying on his right hand side. The perception of depth within otherwise empty regions of space is also made possible through the use of snow. This can help in understanding spatial relationships between objects [6]. The distance of an individual snow particle can be inferred from its apparent angular velocity, and may also be illustrated using intensity based depth cues, or by view disparity in a stereoscopic system. 2.4. Directional illumination It is common for 3D rendering algorithms to include ....

D.N. Lee, "The Optic Flow Field: The Foundation of Vision", Philosophical Transactions of the Royal Society of London, B290, pp.169--179, 1980.

....on the vector line of this drawn vector 4.2 Accelerated Translational motion Consider an observer with translation velocity t at s = 0 and constant acceleration a. The observer moves on a curve: fi(s) st x a x s 2 2 ; st y a y s 2 2 ; st z a z s 2 2 (5) Following Lee [Lee80], Rieger [Rieger83] has shown that the projected collision points can be computed from the time derivatives of the velocity scaled depth. Since the velocity scaled depth entails information about the instantaneous motion, intuitively one can imagine that these derivatives contain information ....

Lee D.N. 1980. The optic flow field: the foundation of vision. Philosophical transactions of the Royal Society of London 290: 169-179.

....by the intersection of the axis of translation with an imaging This research is supported by the Advanced Research Projects Agency of the Department of Defense and is monitored by the U. S. Army Topographic Engineering Center under contract No. DACA76 92 C 0016 surface [ Gibson, 1950; Lee, 1980 ] The technique presented in [ Lawton, 1982 ] was based on optimizing a measure which described the quality of feature matches restricted to lie along the radial flow paths associated with a potential axis of translation. The optimization process involved searching over the surface of a unit ....

D.N. Lee. The optic flow field: The foundation of vision. Philosophical Transactions of the Royal Society of London, Series B, 290:169--179, 1980.

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Denis N. Lee. The optic flow field: The foundation of vision. Philosophical Transactions of the Royal Society of London, Series B, B290:169--179, 1980.

No context found.

Lee D.N. 1980. The optic flow field: the foundation of vision. Philosophical transactions of the Royal Society of London 290: 169-179.

No context found.

Perception, 5, 437-459. Lee, D.N. (1980) The optic flow field: The foundation of vision. Phil. Trans. of the R. Soc. of Lond. B, 290, 169-179.

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Perception, 5, 437-459. Lee, D. N. (1980). The optic flow field: The foundation of vision. Philosophical Transactions of the Royal Society of London B, 290, 169-179.

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