WO2008034195A1

WO2008034195A1 - Optical detection system

Info

Publication number: WO2008034195A1
Application number: PCT/AU2007/001406
Authority: WO
Inventors: Saul Thurrowgood; Dean Dino Soccol; Mandyam Veerambundi Srinivasan
Original assignee: The Australian National University
Priority date: 2006-09-21
Filing date: 2007-09-21
Publication date: 2008-03-27

Abstract

An optical detection system is disclosed, and includes a camera (12) adapted for attachment to a vehicle (10), and a reflective surface (14), also adapted for attachment to said vehicle, and lying in a field of view of said camera (12). The camera (12) captures light emanating from a subject plane (16) parallel to the optical axis (20) of the camera and reflected from said surface as said vehicle (10) moves. The reflective surface (14) has a profile of a variable radius of curvature in at least one plane perpendicular to the subject plane (16) adapted to map equal distances in the subject plane (16) to equal angles in the camera image plane (34). The system also enables the determination of a collision-free cylinder of space (65), centred on the optic axis, through which the aircraft can safely navigate.

Description

Optical detection system

Field of the invention

This invention relates to optical detection systems, and particularly systems to detect characteristics of surfaces at a distance. In one instance, such detection systems are for visual guidance of terrain following and landing in unmanned airborne vehicles (UAVs).

Background

There is considerable interest in designing guidance systems for UAVs that use passive sensing (such as vision), rather than active sensing (such as radar) that can be bulky, expensive and stealth-compromising.

There is growing evidence that flying insects use optic flow cues to regulate flight speed, to estimate and control height above ground, to guide landing, and to avoid obstacles. There is also considerable interest in incorporating this principle to guidance of aircraft (see, for example, M. V. Srinivasan., S.W. Zhang, J S Chahl, G Stange and M Garratt, "An overview of insect inspired guidance for application in ground and airborne platforms", Proc Inst Mech Engnrs Part G, 218, 2004, pp. 375- 388.)

Passive vision systems that are currently used in UAVs for this purpose consist of a downward-looking video camera to measure the optic flow generated by the ground. Such a configuration, while being relatively simple to implement, has practical limitations. During low-altitude terrain following or landing, the image of the ground moves very rapidly, making it difficult to obtain accurate estimates of optic flow. This situation also applies in other fields where optical detection systems are used.

There is thus a need to provide an arrangement that allows an improvement in the determination or estimation of such optic flows. Summary

A system and an associated method are disclosed here that provide a reflective surface of a geometry or profile that produces an image of a subject surface (e.g., terrain) that moves at a constant, low velocity to simplify subsequent optic flow measurements. The effect is achieved by creating a particularly shaped mirror surface that, firstly, scales down the speed of image motion as seen by a camera, and, secondly, removes the perspective distortion (and therefore distortion in image velocity) that a camera experiences when viewing a subject (e.g., a horizontal plane that stretches out to infinity). This is achieved for any given orientation of the mirror with reference to the camera and the subject plane by changing the curvature of the mirror with viewing direction in such a way that the highest curvature is in a section of the mirror having a direction of view that is perpendicular to the closest point of the subject plane.

Therefore, there is provided an optical detection system comprising: a camera adapted for attachment to a vehicle; and a reflective surface, also adapted for attachment to said vehicle, and lying in a field of view of said camera; and wherein said camera captures light emanating from a subject plane substantially parallel to the optical axis of the camera and reflected from said surface as said vehicle moves; and further wherein said reflective surface has a profile of a variable radius of curvature in at least one plane perpendicular to the subject plane adapted to map equal distances in the subject plane to equal angles in the camera image plane.

There is further provided an optical detection system comprising: a camera adapted for attachment to a vehicle; and a reflective surface, also adapted for attachment to said vehicle, and lying in a field of view of said camera; and wherein said camera captures light emanating from a subject plane substantially parallel to the optical axis of the camera and reflected from said surface as said vehicle moves; and further wherein said reflective surface has a profile of a variable radius of curvature in at least one plane perpendicular to the subject plane adapted to map equal distances in the subject plane to equal displacement in the camera image plane. There is yet further provided an optical detection system comprising: a camera adapted for attachment to a vehicle; and a reflective surface, also adapted for attachment to said vehicle, and lying in a field of view of said camera; and wherein said camera captures light emanating from a subject plane substantially parallel to the optical axis of the camera and reflected from said surface as said vehicle moves; and further wherein said reflective surface has a profile with relatively higher curvature in a section of the mirror having a direction of view that is perpendicular to the closest point of the subject plane than other sections of said surface.

One such particular surface geometry maps equal distances along the terrain in the travel direction to equal increments in viewing angle as seen by the camera (i.e., the image moves with constant angular velocity, as seen by the camera). For every degree in change of the direction of view of the camera, the orientation of the corresponding mirror surface changes by an amount such that the reflected ray traverses a constant forward distance along the subject plane, irrespective of the direction of view. This geometry is suitable for a camera with a spherical imaging surface - where it will generate an image that moves with uniform velocity on the spherical surface.

Another such surface geometry maps equal distances along the terrain in the travel direction to equal displacements in the image plane. Here, the curvature of the mirror is such that rays from segments of constant length along the direction of travel on the subject plane project to segments of constant length in the image plane of the camera. This geometry is suitable for a camera with a planar imaging surface - where it will generate an image that moves with uniform velocity on the planar surface.

A method is also provided for facilitating vehicle guidance with respect to a subject plane. The method comprises providing a reflective surface attached to the vehicle, which has a profile that produces an image of the subject plane that moves at a substantially reduced and constant velocity. - A -

Furthermore, there is provided a method for facilitating vehicle collision avoidance when vehicle moves within a surrounding environment. The method comprises the steps of: providing a reflective surface attached to the vehicle, the surface having a profile that produces an image of at least a portion of the surrounding environment, the image moving at a substantially reduced and constant velocity; capturing the image of the at least a portion of the surrounding environment reflected by the reflective surface, by way of a camera also attached to the vehicle; computing the optic flow generated by relative movement between the vehicle and the at least a portion of the surrounding environment; and using a computed magnitude of the optic flow, computing the radial distance of any object in the at least a portion of the surrounding environment from an axis of movement of the vehicle.

Brief description of the drawings

Fig. 1 is a schematic diagram showing an optical detection system on a UAV.

Fig. 2 is a schematic diagram of an optical system for use in the optical detection system of Fig. 1, the optical system including a first mirror profile.

Fig. 3 illustrates the basic geometry of flight variables in the optical detection system of Fig. 1.

Fig. 4 is a schematic diagram of an optical system for use in the optical detection system of Fig. 1, the optical system including a second mirror profile.

Figs. 5A and 5B show a computer simulation for a mirror of the second profile for a forward-facing camera.

Figs. 6A and 6B show a computer simulation for a mirror of the second profile for a rearward-facing camera.

Fig. 7 shows two example mirror types. Fig. 8 shows an example field of view of a forward-facing camera over a ground surface.

Figs. 9 and 10 show the imaging properties of a prism-type mirror.

Fig. 11 shows the imaging properties of a cone-type mirror.

Fig. 12 is a remapped view of the image of Fig. 11.

Fig. 13 shows the image produced by a cone-type mirror for flight over water.

Fig. 14 is a remapped view of the image of Fig. 13.

Fig. 15 shows computed optic flow.

Fig. 16 is a remapped view of the computed optic flow of Fig. 15.

Figs. 17 and 18 show computed optic flow vectors for a test in which the vision system was moved by a robotic gantry over a visually textured horizontal plane at constant height and velocity.

Figs. 19 and 20 show plots of mean optic flow as a function of height and proximity, respectively.

Figs. 21 and 22 show plots of the horizontal component of mean optic flow as a function of height and proximity, respectively.

Fig. 23 shows a view of the system installed on the underside of the fuselage of a model aircraft.

Fig. 24A shows a raw image and Fig. 24B shows the computed optic flow vectors in the remapped image from a test flight, at a relatively high altitude. Fig. 25A shows a raw image and Fig. 25B shows the computed optic flow vectors in the remapped image from a test flight, at a relatively low altitude.

Fig. 26 illustrates how the geometrical mapping that is produced by the vision system can be used to determine the radius of a collision-free cylinder.

Detailed description

Fig. 1 shows, in exaggerated form, a UAV 10 having an optical detection system formed by a video camera 12 and a mirror 14. The direction of flight of the UAV 10 is indicated. The mirror 14 also can be referred to more generally as a 'reflective surface'. The UAV 10 is flying at a height above a subject (ground) plane. The ground plane 16 is approximated in the diagram as being flat, but, of course, most usually it is not perfectly flat. The effective field of view of the camera 12 of the ground plane 16 is indicated by the ray tracing lines 18. Ideally, the moving image of the terrain 16 that is captured by the camera 12 through the mirror 14 should exhibit a constant, low velocity everywhere, thus simplifying subject optic flow measurements, and increasing their accuracy, when used to guide flight of the UAV 10. The camera 12 captures light emanating from the ground plane 16 and reflected by the mirror 14 without disruption of the optical path.

Mirror profiles

As already noted, the mirror is shaped to scale the speed of image motion and remove perspective distortions. Broadly speaking, this is achieved by making the local curvature of the mirror change with viewing direction to achieve a desired mapping. The ground directly beneath the aircraft is closest to the imaging system and is perpendicular to the direction of view from the mirror. A unit distance on this section of the ground therefore subtends the largest angle at the mirror, so the mirror needs to have the highest curvature for imaging this section in order to compress the image as seen by the camera. On the other hand, the ground in front of or behind the aircraft is much further away and is viewed obliquely. So the mirror has lower curvature (less compression) for imaging these sections. The result is that the mirror maps all regions of the horizontal plane uniformly. Two forms of mirror will now be described.

Mirror profile 1

Mirror profile 1 maps equal distances along the ground in the flight direction to equal increments in viewing angle, as seen by the camera 12. For every degree in change of the direction of view of the camera, the orientation of the corresponding mirror surface changes by an amount such that the reflected ray traverses a constant forward distance along the ground plane, irrespective of the direction of view. This geometry is suitable for a camera with a spherical imaging surface — where it will generate an image that moves with uniform velocity on the spherical surface.

The camera-mirror configuration is shown in Fig. 2. The optical axis 20 of the camera 12 is horizontal. A ray from a point 'A' on the ground is reflected by the mirror surface 24 into the camera 12. For convenience of analysis, the ray paths are shown reversed: they are depicted as leaving the camera 12 from the nodal point 22, and being reflected by the mirror surface 24 onto the point A on the ground 16. This is in accordance with the principle of reversibility of optical paths.

The profile of the mirror is such that, as the aircraft 10 flies at a constant speed, the image of a point on the ground 16 (e.g. A), as viewed by the camera 12 through the mirror 14, has a constant angular velocity. That is,

— = K dt

where K is a constant, independent of θ. The smaller the value of K, the smaller the angular velocity of the image of this point A in the camera 12.

The direction of the ray incident on the mirror surface 24 (relative to the horizontal), is denoted by the variable θ (radians), the direction of the reflected ray by the variable β (radians), and the distance between the camera nodal point 22 (O) of the camera lens 26 and the point of reflection on the surface (P) by the variable r. The directions of the incident and the reflected rays at the point P are then related by

where the quantity represents the angle between the incident ray OP and

the tangent to the mirror profile at the point P, and the factor 2 accounts for the fact that the reflected ray deviates from the incident ray by twice this angle (Snell's law).

. -1 / dθ_^

Denoting the quantity 2. tan (r — ) by ω, (1) is rewritten as dr

β = θ + ω (2)

Note that ω represents the angular deflection that the incident ray OP from the camera 12 undergoes after reflection at the mirror surface 24: it is the change in direction between the ray OP and the ray PA.

Consider the rate of change of β with time

dβ_ ₌ dβ_ dθ_ dt dθ ^' dt ^{K }}

As mentioned above, the image of the point A in the camera is wanted to move at a constant angular velocity. That is

^ = K (4) dt ^{K J}

where K is a constant, independent of θ.

From (2), one obtains

"I = I ₊ ^ (5) dθ dθ ^{κ J}

Inserting (4) and (5) into (3), gives

Fig. 3 illustrates the basic geometry of flight variables. V denotes flight velocity, h the height above the ground 16, and β is the direction of view of a Point A on the ground surface 16. X denotes the horizontal distance of this point from a point on the ground 16 directly below the aircraft's imaging system 12, 14. From Fig. 3, it is clear that the rate at which β changes with time will depend upon the speed of the aircraft (V) scad its height (h) above the ground. From this figure

tan/? = - (7) x

where X denotes the horizontal distance between the aircraft and the point A on the ground at time t. Differentiating (7) with respect to time, gives

dx

Noting that — = -V , (8) may be rewritten as dt

s_Q^ -^>β..^.^ = -^.(-v) = (-).(-r (9) d£t .^, -4 x .H0 -A h (V x

Inserting (7) into (9), gives

which can be rearranged to obtain

f dt = £ h -.'/». (H)

Inserting (2) into (11) gives -f- = ^.sin² (0 + ω) (12) at h

Combining (6) and (12), gives

which can be rewritten to obtain

— = — sm² {θ + ώ) -\ (14) dθ K.h ^{K } V} '

Equation (14) is a differential equation that describes the profile of the mirror. It can be integrated numerically with respect to θ to obtain a result of the form

ω = G(θ) + ψ (15)

where G is a function of θ (G(O) = O) and ψ is a constant of integration that is determined by a boundary condition. Recalling that ω represents the angular deflection that the incident ray from the camera undergoes after reflection at the mirror surface, ψ can be determined by prescribing the deflection of any one of the rays from the camera that is incident on the mirror surface. If one chooses the on-axis ray, for example (θ = 0), and prescribe that this ray should be reflected straight back toward the camera, one has the boundary condition ω = π when 0 = 0. (This is a situation in which the surface of the mirror is orthogonal to the on-axis ray from the camera at the point of interception.) As another example, if the on-axis ray is required to be deflected by 90 deg (that is, the axial camera ray looks directly below the aircraft 10), then one has the boundary condition ω = — when θ = 0. In general, the boundary condition ω = ω₀ when θ = 0 leads to ψ = ω₀ - G(O) = ω₀.

Thus, the general solution for the mirror profile is:

ω = G(θ) +ω_o= H(θ) (16) where H(θ) ≡ G(θ) +ω₀

The next step is to integrate (16) numerically to obtain a relationship between r and θ, which will specify the profile of the mirror in polar co-ordinates with the origin at the nodal point 22 of the camera lens 26. Noting thatω = 2.tan^~' (r — ) , re-express (16) dr as

. ., , dθ. H(θ) tan (r — ) = — ^^ (17) dr 2

or

(18) rdθ 2

where J{β) = -^M . (19)

Thus

— = cot(J(θ)).dθ = F(θ).dθ (20) r

where F(θ) ≡ cot(J(θ)) (21)

Integration of (20) gives

log_e r = ^F(θ).dθ + B (22)

where e^B is a constant of integration that depends upon a second boundary condition, namely, the on-axis distance ^Q of the mirror surface 24 from the nodal point 22 of the camera lens 26. Setting r = ro at θ = 0, one obtains e = r₀ . Thus, the profile of the mirror is described in polar co-ordinates (r, θ) by the function

G(θ) + ω₀ where TQ is the desired on- axis distance of the mirror and F(θ) = cot m

2 which G(θ) is the numerically-integrated solution to differential equation (14) , and ω₀ is desired angular deflection of the on-axis ray. Other parameters that determine the profile of the mirror are: the velocity of the aircraft (V), the height of the aircraft (h), and the desired angular velocity of the camera image, K. These parameters enter the solution through the differential equation (14).

Mirror profile 2

Mirror profile 2 maps equal distances along the ground in the flight direction to equal displacements in the image plane of the camera. Here, the curvature of the mirror is such that rays from segments of constant length along the flight direction on the ground plane project to segments of constant length in the image plane of the camera. The geometry of this mirror therefore is slightly different from that of mirror profile 1 specified above because this mirror also compensates for the additional distortion that arises from the fact that equal changes in the direction of view of the camera do not map into equal changes of position in the planar image of the camera. (Except when the angular field of view of the camera is very small, when this additional distortion becomes negligible and the two mirrors approach identicality).

The camera-mirror configuration is shown in Fig. 4. The mirror 30 has a profiled surface 32. A' is the camera image, lying in the camera image plane 34, of a point A on the ground 16. The outline of the camera and camera lens has been omitted for clarity.

In this design it is desired that A' (the image of A) moves at a constant velocity in the image plane 34 of the camera, independent of the position of A in the ground plane 16. That is, it is required that ^L = L (25) dt

where r\ is the distance of the point A' from the centre of the camera's image plane 34, and L is the desired constant velocity. One has

η = /.tan θ (26)

where / is the focal length of the camera. Differentiating (26) with respect to time obtains

dη ₂ dθ

— - = /.sec θ. — (27) dt dt

Combining (25) and (27) gives

L = f.sec² θ. — (28) dt

which can be rearranged to obtain

dθ L cos ² θ (29) dt ^~ /

Note that

dβ _ dβ_ dθ

(30) d dtt d dθθ ^' d dtt

Inserting (5) and (29) into (30), obtains

Combining ( 12) and (31 ), obtains dω

— .sin² (6> + 6)) = 1 + .-.cos² 0 (32) h ^~dθ /

which can be rewritten as

The remainder of the derivation proceeds as in the case of Mirror Profile 1.

The differential equation (33) is integrated numerically to obtain a relationship between ω and θ of the form

ω = G₁ (θ) +ω₀ (34)

where G₁(Z?) is the numerically integrated solution of (33) and ωo is determined by the boundary conditions, as described for Profile 1.

Proceeding further as in the case of Profile 1, it can be shown that the Mirror profile 2 is described (in polar co-ordinates) by the expression

G_x (θ) + ω₀ where TQ is the desired on-axis distance of the mirror and F₁ (θ) = cot

in which G₁(^) is the numerically-integrated solution to differential equation (33) , and ω₀ is desired angular deflection of the on-axis ray. Other parameters that determine the profile of the mirror are: the velocity of the aircraft (V), the height of the aircraft Qi), the focal length of the camera (/), and the desired linear velocity of the image in the camera, L. These parameters enter the solution through the differential equation (33). Substantiation

Fig. 5A shows an example of a mirror 40 (i.e., embodying mirror profile 2) as a computer reconstruction. In this example, the camera faces forward. Dimensions are in cm. The nodal point 42 of the camera is at (0.0). The image plane of the camera is to the left of the nodal point 42 and is not shown in the figure, but its reflection about the nodal point (i.e., an equivalent representation) is depicted as the vertical line 44 to the right of the nodal point 42. Parameters used in this design simulation are: V=100.0 cm/sec; h=100.0 cm; r₀=10.0 cm; f=3.5 cm; L=0.2 cm/sec. The curvature of the mirror 40 is highest in the region that images the ground directly beneath the aircraft, because this is the region of the ground that moves at the highest angular velocity with respect to the camera, and which therefore requires the greatest scaling down of motion. The variation of mirror curvature is illustrated in Fig. 5B, which shows how the local curvature of the surface varies with the direction of the exit ray (β in Fig. 2). The local curvature is measured in terms of the curvature index, defined as the ratio of the incremental change in the direction of the tangent to the mirror surface to the incremental change in the direction of the camera ray (θ in Fig. 2). It is evident that the curvature index is a maximum when the exit angle is 90 deg. As is apparent from the ray tracing, equally spaced points on the ground along the line of flight map to equally spaced points in the camera image (i.e., as appears at line 44, equivalent to the camera image plane).

Fig. 6 shows another example of the second profile mirror 50. In this example, the camera faces rearward. The camera nodal point 52 is again at (0,0). The design parameters are: V=IOO.0 cm/sec; h=100.0 cm; ro=lO.O cm; f=3.5 cm; L=O.14 cm/sec. The equivalent camera image plane is shown again by a vertical line 54. The variation of mirror curvature for this example is illustrated in Fig. 6B. Here, again, the curvature index is a maximum when the exit angle is 90 deg. Equally spaced points on the ground along the line of flight map to equally spaced points in the camera image. This design with the rear-facing camera has the advantage that the requisite mirror has a smaller depth and a smaller maximum radius for coverage of the same area on the ground. The overall system would thus be lighter and more compact. Prism-type and cone-type mirrors

There are two types of mirrors that can be designed, each of which can incorporate either of the above profiles.

Prism-type mirror

This mirror incorporates one of the above profiles along one axis and is flat along the orthogonal axis. An example of a prism-type mirror is shown on the left side of Fig. 7. This image and subsequent images and visualizations were created using POVRAY™, ["Persistence of Vision Rαytrαcer", a software ray-tracing simulation and visualization package available from http ://www.ρo vray . org/] .

Cone-type mirror

This mirror is circularly symmetrical, and is generated by rotating one of the above profiles about the z axis. An example of a cone-type mirror is shown on the right side of Fig. 7.

In order to illustrate the imaging properties of these mirrors, consider the view that would be obtained from a forward-facing camera mounted beneath an aircraft 10, as shown in Fig 1, without the use of any mirror. Fig. 8 depicts such a view, in which the ground 16 carries a checkerboard texture. The field of view of the camera is 70 deg (horizontal) x 52.5 deg (vertical). The perspective distortion (progressive foreshortening of distant checks) is clearly evident. This means that, for straight and level flight, the magnitude of the vertical component of optic flow will be greatest at the bottom of the image, and lowest near the horizon.

Fig. 9 illustrates the imaging properties of a prism-type mirror, positioned with its axis parallel to and above a plane carrying a checkerboard pattern. Note that the mirror has removed the perspective distortion (foreshortening): All checks in the mirror image have the same height. This means that, for straight and level flight, all regions of the image will have the same vertical velocity. This simplifies and reduces the computation of optic flow to one dimension. Note also that the mirror endows the camera with a larger field of view, covering regions in front of the aircraft as well as behind it. The horizontal line in Fig. 9 represents viewing directions at 90 deg to the camera's optical axis: looking straight down below the aircraft, and to either side. Regions of the image below this line represent areas in front of the aircraft, and regions above the line represent areas behind the aircraft. In contrast, the direct image from the camera (without the mirror) covers a relatively small forward-looking visual field, as shown in Fig. 8.

The prism-type mirror, while providing some of the desired mapping properties, carries a slight disadvantage: the mapping is distorted when the imaging system is rotated about its optic axis, i.e. when the aircraft rolls (e.g. at 45 degrees to the left), as shown in Fig. 10. The disadvantage may be tolerated in some instances, but if not is eliminated by use of the cone-type mirror.

Fig. 11 illustrates the imaging properties of a cone-type mirror, positioned with its axis parallel to and above a plane carrying a checkerboard pattern. Note that the mirror has removed the perspective distortion (foreshortening). However, the scale of the mapping depends upon the radial direction. Compression is lowest in the vertical radial direction and highest in the horizontal radial direction. This means that, for straight and level flight parallel to the ground plane, the optic flow vectors will have constant magnitude along each radius but will be largest along the vertical radius and smallest (zero) along the horizontal radius.

It is clear that rotation of this imaging system about the optic axis will not distort the image — it will simply rotate the image through the same angle in the opposite direction. Thus, the optic flow pattern is robust to changes in the roll attitude of the aircraft. In fact, the flow pattern can be used to extract information on the roll attitude - the radius of maximum optic flow will point directly to the ground.

The cone-type mirror also endows the camera with a larger field of view, covering regions in front of as well as behind the aircraft. The circle in Fig. 11 represents viewing directions at 90 deg to the camera's optical axis: looking straight down below the aircraft, to either side, and upwards at the sky. Regions of the image outside this circle represent areas in front of the aircraft, and regions inside the circle represent areas behind the aircraft. Fig. 12 shows a digitally remapped view of the image in Fig. 11, in which the polar co-ordinates of each pixel in Fig. 11 are plotted as Cartesian co-ordinates. Here, the vertical axis represents radial distance from the centre of the image of Fig 11, and the horizontal axis represents the angle of rotation about the optic axis. The circle shown in Fig. 11 maps to the horizontal line shown in Fig. 12. Regions below the line represent areas in front of the aircraft, and regions above it areas behind.

The description that follows deals only with the cone-type mirror. Fig. 13 shows the image produced by a cone-type mirror with the same parameters as the mirror in Fig. 11, except that the ground texture is now that of an ocean. Fig. 14 shows a digitally remapped version of this image.

Optic flow computations

An Image Interpolation algorithm was used with image sequences produced by the mirror systems described herein. Specifically, an iterative image interpolation algorithm, which produced increasingly accurate estimates of optic flow in successive iterations using a coarse-to-fine baseline procedure, was used. Such an algorithm is developed, for example, in M.V. Srinivasan, "An image-interpolation technique for the computation of optic flow and egomotion". Biological. Cybernetics 71, 1994, pp. 401 -416, the content of which is incorporated herein by reference.

An example of the results obtained using this algorithm is shown in Fig. 15. It is evident that the magnitude of the flow is much lower in the mirror image, than it is from the direct camera view to the ocean. Within the mirror image the flow is primarily radially inwards, with the largest magnitude occurring along the lower vertical radius, as expected. The region above the horizon (the sky) generates no optic flow, as it is infinitely distant from the camera and the camera motion is along a straight line. The flow vectors are erroneous in some areas. Within the mirror image, errors in the flow computation arise as a result of specular reflections from the ocean surface. The errors near the boundary of the mirror are due to the presence of a discontinuity in the motion across the boundary.

Fig. 16 shows optic flow computed on the remapped image sequence. Here, all flow vectors in the ocean are directed vertically, with the largest magnitudes occurring along the centre column (which corresponds to the strip of ocean directly under the aircraft, along the direction of flight). The sky, as before, generates no optic flow.

Test of system on a robotic gantry The vision system described in Fig. 5 was fabricated and mounted on the arm of a computer-controlled gantry. The system was moved over a visually textured plane at a speed of 20 cm/sec at various heights, and image sequences were acquired at a rate of 25 frames/sec. The texture was a random array of black/white pixels, with each pixel of size 1 cm x 1 cm. Each video frame was 800 x 300 pixels. Optic flow computations were carried out on the remapped image sequence. The optic flow was computed using a two-stage image interpolation algorithm, with a reference shift of 8 pixels, a filter width of 16 pixels, and a flow patch window size of 64 x 64 pixels.

The results of the optic flow calculations for flight heights of 7.3cm and 13.3 cm are shown in Figs. 17 and 18, respectively. Note, in Fig. 17, that the flow magnitudes are greatest in the central column and fall off to either side. Only the ground generates optic flow. There is very little flow in the rest of the visual field (dark areas in the left and right-hand margins) because objects in the areas are much farther away from the vision system. Note, in Fig. 18, that at this higher altitude, the flow magnitudes are lower.

Fig. 19 illustrates the variation in the magnitude of the vertical component of optic flow in the remapped image sequences, as a function of the height of flight. AU of these measurements were made at a constant gantry speed of 20 cm/sec. Optic flow is shown in terms of mean pixel shift in the central column. It is evident that the magnitude of the optic flow varies approximately inversely with height above the surface (Z). Thus, one would expect the flow magnitude to increase linearly with reciprocal of height (or proximity to the ground). Fig. 20 shows that this is indeed the case.

Fig. 21 illustrates the variation in the magnitude of the horizontal component of optic flow in the remapped mages, as a function of height. Fig. 22 shows the same data as a function of proximity (reciprocal of height). It is clear that the horizontal component is very small compared to the vertical component. Ideally, the horizontal component would be zero if the system moves precisely along the direction of its optical axis. The existence of the small horizontal component is indicative of a small amount of misalignment, hi practice, this will not pose a problem because the horizontal component of the flow pattern exhibits the same properties as the vertical flow pattern, so that a proper estimate of the flow magnitude can be obtained by computing the mean magnitude of the 2D flow vectors.

If the alignment of the optical system is perfect, then the presence of a lateral component in the optic flow will signal sideways drift, for example due to wind, and would enable appropriate compensatory control.

Table 1 gives the means and standard deviations of the optic flow measurements.

Table 1 Flight tests

A prototype of the vision system, using a rearward-facing camera, was mounted on the underside of the fuselage of a model aircraft shown in Fig. 23.

Fig. 24A shows a raw image and Fig. 24B shows the computed optic flow vectors in the remapped image from a test flight of the model aircraft, at a relatively high altitude.

Fig. 25A shows a raw image and Fig. 25B shows the computed optic flow vectors in the remapped image from a test flight of the model aircraft, at a relatively low altitude. Collision avoidance embodiment

The flow vectors thus calculated can be used to obtain information on the distance to the ground as well as to objects on either side of the aircraft, and above it. Referring to Fig. 26, an aircraft 60, incorporating a vision system 62, flies along a flight axis 64. The special geometry of the mapping that is achieved by the mirror means that, for any given aircraft speed, the radial distance of any object in the environment from the axis of flight (R) is determined by the magnitude of the optic flow that it produces (computed by a suitable processor) in the image captured by the mirror. In other words, if a cylinder of "free space" is desired for collision-free flight along a given trajectory, the maximum permissible flow magnitude is determined from the speed of the aircraft and the radius of this cylinder. This simplifies the problem of determining in advance whether an intended flight trajectory through the environment will be collision-free, and of making any necessary adjustments to the trajectory to ensure collision-free flight. Thus, the system also enables the determination of a collision- free cylinder of space (65), centred on the optic axis, through which the aircraft can safely navigate.

It would be apparent to a skilled addressee that the above described embodiments of an optical detection system are associated with a corresponding method for facilitating vehicle guidance with respect to a subject plane, in particular, and within a surrounding environment, in general. Here it should be noted that the general discussions in this specification refers to a substantially horizontally flying UAV, where the optical axis of the attached camera is parallel to the subject plane. However, it should be appreciated that the main principles of the discussed imaging system are well applicable also in situations where the aircraft is only approximately parallel to the surface.

Other applications Whilst the example embodiments of the optical detection system described in this specification refer to UAVs, the principles apply equally to the other applications of optical detection systems, such as:

• Monitoring traffic flow from overhead; • Measuring self-motion (e.g., car speed, boat speed, train speed);

• Determining road profile (e.g., camber);

• Measuring conveyor belt throughput by height profiles;

• River flow measurement; • Depth profiling of a boat over clear water; and

• Corridor and tunnel navigation and surveillance.

It should be appreciated that the above described optical detection system operates on the basis of measuring the optical flow generated upon a relative movement between the camera and the surrounding environment. Accordingly, the functionality of the optical detection system in applications in which the detection system is stationary, however at least a portion of the surrounding environment (such as a car) is moving, is not substantially different from the operation described for the "airplane" scenario.

Claims

Claims:

1. An optical detection system adapted for attachment to a supporting body, the system comprising: a camera; and a reflective surface lying in a field of view of said camera; and wherein said camera captures light emanating from a subject plane substantially parallel to the optical axis of the camera and reflected from said surface, upon a relative movement between said body and at least a portion of said subject plane; and further wherein said reflective surface has a profile of a variable radius of curvature in at least one plane perpendicular to the subject plane, the profile being adapted to map equal distances in the subject plane to equal angles in the camera image plane.

2. An optical detection system adapted for attachment to a supporting body, the system comprising: a camera; and a reflective surface lying in a field of view of said camera; and wherein said camera captures light emanating from a subject plane substantially parallel to the optical axis of the camera and reflected from said surface, upon a relative movement between said body and at least a portion of said subject plane; and further wherein said reflective surface has a profile of a variable radius of curvature in at least one plane perpendicular to the subject plane, the profile being adapted to map equal distances in the subject plane to equal displacements in the camera image plane.

3. An optical detection system adapted for attachment to a supporting body, the system comprising: a camera; and a reflective surface lying in a field of view of said camera; and wherein said camera captures light emanating from a subject plane substantially parallel to the optical axis of the camera and reflected from said surface, upon a relative movement between said body and at least a portion of said subject plane; and further wherein said reflective surface has a profile with relatively higher curvature in a section of the mirror having a direction of view that is perpendicular to the closest point of the subject plane than other sections of said surface.

4. An optical detection system as claimed in claim 3, wherein said profile is adapted such that for every degree in change of the direction of view of the camera, the orientation of the corresponding mirror surface changes by an amount such that the reflected ray traverses a constant forward distance along the subject plane, irrespective of the direction of view.

5. An optical detection system as claimed in claim 3, wherein said profile is adapted such that rays from segments of constant length along the camera's direction of view on the subject plane project to segments of constant length in the image plane of the camera.

6. An optical detection system as claimed in any one of the preceding claims, including a processor to compute optic flow vectors from an output signal of said camera.

7. An optical detection system as claimed in any one of the preceding claims, wherein the supporting body is a vehicle moving with respect to the subject plane.

8. A reflective surface for application in the optical detection system of claim 1, the reflective surface having a profile of a variable radius of curvature in at least one plane perpendicular to the subject plane adapted to map equal distances in the subject plane to equal displacement in the camera image plane.

9. A reflective surface for application in the optical detection system of claim 1, the reflective surface having a profile of a variable radius of curvature in at least one plane perpendicular to the subject plane adapted to map equal distances in the subject plane to equal displacement in the camera image plane.

10. A reflective surface for application in the optical detection system of claim 1, the reflective surface having a profile with relatively high curvature in a section of the reflective surface having a direction of view that is perpendicular to the closest point of the subject plane than other sections of said surface.

11. A vehicle including an optical detection system as claimed in any one of claims 1 to 7, or a reflective surface, as claimed in any one of claims 8 to 10.

12. An aircraft collision avoidance system including an optical detection system as claimed in any one of claims 1 to 7, or a reflective surface, as claimed in any one of claims 8 to 10.

13. A method for facilitating vehicle guidance with respect to a subject plane, the method comprising providing a reflective surface attached to the vehicle, the surface having a profile that produces a reflected image of the subject plane, the reflected image moving at a substantially reduced and constant velocity.

14. The method of claim 13, wherein the profile of the reflective surface is arranged to; scale down the speed of image motion of the subject plane, as seen by a camera being also attached to the vehicle, and remove the perspective distortion experienced by the camera when viewing the subject plane.

15. The method of claim 14, wherein the profile of the reflective surface is changed with viewing direction in such a way that the highest curvature is in a section of the reflective surface having a direction of view that is perpendicular to the closest point of the subject plane.

16. The method of any one of claims 13 to 15, further comprising computing the optic flow generated by relative movement between the vehicle and the subject plane.

17. A method for facilitating vehicle collision avoidance when a vehicle moves within a surrounding environment, the method comprising the steps of; providing a reflective surface attached to the vehicle, the surface having a profile that produces an image of at least a portion of the surrounding environment, the reflected image moving at a substantially reduced and constant velocity; capturing the reflected image of the at least a portion of the surrounding environment by way of a camera, also attached to the vehicle; computing the optic flow generated by the relative movement between the vehicle and the at least a portion of the surrounding environment; and using a computed magnitude of the optic flow, computing the radial distance of any object in the at least a portion of the surrounding environment from an axis of movement of the vehicle.

18. The method for facilitating vehicle collision avoidance of claim 17, wherein the portion of the surrounding environment comprises a subject plane substantially parallel to the direction of movement of the vehicle.

19. The method for facilitating vehicle collision avoidance of claim 17, the method further comprising the step of determining a collision-free cylinder of space, centred on an optical axis of the camera, through which the vehicle can navigate substantially safely.

20. The method for facilitating vehicle collision avoidance of any one of claims 17 to 19, wherein the vehicle is an aircraft.