WO2000042470A1 - Imagerie panoramique invariante en resolution - Google Patents

Imagerie panoramique invariante en resolution Download PDF

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Publication number
WO2000042470A1
WO2000042470A1 PCT/AU2000/000022 AU0000022W WO0042470A1 WO 2000042470 A1 WO2000042470 A1 WO 2000042470A1 AU 0000022 W AU0000022 W AU 0000022W WO 0042470 A1 WO0042470 A1 WO 0042470A1
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WO
WIPO (PCT)
Prior art keywords
view
reflective surface
panoramic
mirror
imaging system
Prior art date
Application number
PCT/AU2000/000022
Other languages
English (en)
Inventor
John Barratt Moore
Tanya Louise Conroy
Original Assignee
The Australian National University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by The Australian National University filed Critical The Australian National University
Priority to AU24249/00A priority Critical patent/AU757227B2/en
Priority to JP2000593986A priority patent/JP2002535700A/ja
Priority to EP00902499A priority patent/EP1151349A1/fr
Publication of WO2000042470A1 publication Critical patent/WO2000042470A1/fr

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Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B13/00—Optical objectives specially designed for the purposes specified below
    • G02B13/06—Panoramic objectives; So-called "sky lenses" including panoramic objectives having reflecting surfaces
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03B—APPARATUS OR ARRANGEMENTS FOR TAKING PHOTOGRAPHS OR FOR PROJECTING OR VIEWING THEM; APPARATUS OR ARRANGEMENTS EMPLOYING ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ACCESSORIES THEREFOR
    • G03B37/00—Panoramic or wide-screen photography; Photographing extended surfaces, e.g. for surveying; Photographing internal surfaces, e.g. of pipe

Definitions

  • This invention relates to generating wide angle images of spaces, generally referred to as panoramic imaging.
  • Panoramic imaging is becoming an important tool in the area of mobile robotics and machine vision.
  • One simple method involves having a series of cameras mounted on a ring to give views around the entire 360° of horizon. This involves, say, four cameras if they each have a field of view of 90° and some integration of images.
  • There are also a number of single camera methods for panoramic imaging including rotating a camera about its vertical axis and taking pictures continuously to obtain a full panoramic view.
  • Another approach uses wide angle lenses to achieve a large field of view, but these lenses are heavy, expensive and distort the image.
  • An attractive approach to panoramic imaging is to mount a single fixed camera under a curved reflective surface covering a hemisphere such as with a conical, spherical, hyperboloidal, or other profile.
  • the optical axis of the camera is aligned with the central axis of the mirror.
  • a known family of constant gain reflective surfaces have the advantage that they can produce large fields of view such as for a hemispherical or hyperboloidal mirror yet preserve a linear relationship between changes in angles of incidence and reflection of light rays viewed by the camera. This linear relationship simplifies image processing and ensures constant elevational resolution of the image.
  • the shape of the surface is determined by the gain of the linear relationship.
  • the surface is a cone; for higher gains, the surface is specified by a family of polynomial functions.
  • the panoramic plane will be considered as being horizontal and the field of view as vertical as would be the case for a robot moving in a horizontal plane. It will be apparent that in the general case orientation of the planes is arbitrary. All the mirror shapes mentioned above share a common draw back. That is that the CCD cameras used for imaging invariably have uniform Cartesian arrays of pixels to capture the polar image of the scene, and so the pixel density per solid angle increases with the radius of the polar image.
  • the unwarping process transforms the image from polar to Cartesian coordinates so that the angular coordinate in the original polar image maps to the x-coordinate in the unwarped image while the radial coordinate maps to the y-coordinate.
  • the pixel density in the unwarped image varies from low for small x values which correspond to the centre of the original image to high for large x values which correspond to the outer rim of the polar image.
  • Figure 1 shows the unwarping of an image captured with a hyperboloidal mirror. The variation in image quality is clearly evident in the unwarped version.
  • this invention provides a panoramic imaging system including an imaging device having an image plane and a first field of view, a first reflective surface having at least one circularly symmetric portion convex in a radial direction disposed in said first field of view to provide an expanded panoramic second field of view, the profile of the or each convex portion providing a varying gain between the fields of view in the radial direction to limit variation in the solid angle of view across the image plane of the imaging device.
  • the profile of the convex portion provides a substantially uniform solid angle of view across the image plane. That is, the shape ensures that the resolution in the image is invariant to changes in elevation.
  • the shape of the reflective surfaces results in solid angle pixel density invariance.
  • r is the radial distance from the reflective surface to the imaging device
  • ⁇ is the angle from the optical axis of the imaging device ( ⁇ ) is the mirror gain given by
  • ⁇ and ⁇ are the maximum and minimum elevations viewed ⁇ and ⁇ are the maximum and minimum radial angles imaged.
  • r can be plotted against ⁇ at selected intervals to describe the profile by solving the above equation for selected values of ⁇ . For example determining values of r for incremental values of ⁇ of about 1/5° has been found to produce a sufficiently accurate profile for practical application.
  • panoramic range finding There are a number of methods for panoramic range finding.
  • One method uses a cone mirror above a camera.
  • the camera mirror assembly is either displaced during image collection, or two camera mirror assemblies are used to obtain the two views necessary for range finding.
  • this method provides range information in the horizontal plane at video rates, its drawbacks are that no range information is available in the vertical (elevation) direction, objects must be more than a minimum distance from the camera and there may be a blind spot due to the second camera system.
  • a discontinuous, axially symmetric mirror which is in essence a coaxial mirror pair, mounted above a camera to obtain two views of a panoramic scene for stereo disparity range finding is known.
  • known constant gain mirror profiles have been generalised to derive a family of such coaxial mirror pair profiles for panoramic stereo imaging and processing based on disparities in the vertical plane.
  • this invention provides for range finding using a panoramic imaging system containing two resolution invariant mirrors.
  • the mirror or reflector surface has at least two of said convex portions arranged to respectively provide at least partially overlapping panoramic second fields of view for range determination.
  • the second fields of view are preferably substantially co-incident.
  • the two convex portions form a continuous mirror or reflective surface.
  • this invention provides a design for a back to back stereo mirror system with the desirable property of equal pixel sharing between two cameras and thus the two stereo images.
  • the stereo cone in this case is preferably symmetric in the directions orthogonal to the camera axis which is a desirable property for some applications.
  • the imaging system preferably includes two first reflective surfaces each having an associated image plane with corresponding first fields of view, and at least one convex portion of each first reflective surface providing respective panoramic second fields of view, said first reflective surface being arranged back to back such that said reflective second fields of view at least partially overlap.
  • a second reflective surface can, in some applications be interposed between the image plane and the second reflective surface. This allows positioning of the imaging device for example behind the first reflective surface. In some variations an apperture can be provided in the first reflective surface to provide the first field of view from the imaging device.
  • this invention provides a reflective surface for use in a panoramic imaging system including an imaging device having an imaging plane and a first field of view, said reflective surface having at least one circularly symmetric portion convex in a radial direction with a profile providing varying gain in the radial direction between an expanded panoramic second field of view provided by the reflective surface and the first field of view to limit variation in the solid angle of view across the image plane of the imaging device.
  • this invention provides mirrors having minimal intrusive designs, which intrude to a minimal extent into the viewing "hemisphere". These are also termed forward facing designs. They involve an additional planar mirror and camera relocation within the primary reflective surface. The attraction of this arrangement is that the first reflective mirror surface profile is the same design as in a more conventional arrangement.
  • Figure 1 illustrates an unwarping process for a prior art panoramic imaging system
  • Figure 2 schematically shows the relationship between camera image and horizontal view direction in a panoramic imaging system
  • Figure 3 illustrates geometric relationships between a reflecting surface and a camera used to derive mirror profiles according to this invention
  • Figures 4 A and 4B are graphs showing a comparison of a constant gain mirror with a variable gain mirror used in the imaging system according to this invention
  • Figures 5 A and 5B shows ray traced scenes respectively reflected in constant and variable gain mirrors
  • Figures 6A and 6B graphically illustrates a comparison of panoramic imaging systems respectively utilising double constant and variable gain mirror configurations
  • Figures 7 A and 7B shows raced traced images of scenes respectively corresponding to panoramic imaging systems utilising double constant and variable gain mirror configurations
  • Figure 8 schematically illustrates relationships between camera and reflective surfaces used in range calculation utilising a resolution invariant double mirror according to this invention
  • Figure 9 schematically illustrates a back to back mirror configuration according to this invention.
  • Figure 10 schematically illustrates a double back to back mirror configuration according to this invention
  • Figure 11 schematically illustrates a forward looking panoramic imaging system according to this invention.
  • Figure 12 shows a system utilising a combination of the arrangements in Figures 10 and 11.
  • resolution invariance is achieved by adjusting the mirror profile to image relatively less of the scene in the centre of the image and relatively more at the perimeter. That is, a mirror profile is selected to maintain a constant relationship between the pixel density and the angle of elevation in the scene or more precisely, the solid angle.
  • the mirror gain is the relationship between the change in elevation of rays incident on the mirror and the change in the angle of rays reflected into the camera as follows
  • Figure 3 schematically shows an imaging system including an imaging device in the form of a camera having an image plane and a first field of view.
  • a reflective surface or mirror is ... in the first field of view to provide an expanded panoramic second field of view.
  • the surface is circularly symmetric and convex in a radial direction.
  • ⁇ is a function of image angle ⁇ (related to the radial coordinate in the image, p) so (4) becomes
  • the radius in the image, p is related to the radial angle of a ray reflected from the mirror, ⁇ by the focal length of the camera, / (a constant)
  • the image pixel density be invariant to angle of elevation in the scene which leads to more of the scene being imaged towards the perimeter, so
  • Figures 4A and 4B show for comparison a constant gain mirror and a variable gain mirror with the same camera field of view and range of elevations imaged.
  • the rays shown are constantly spaced in ⁇ , with about 2° between each ray. It is clear from Fig. 4A that in the constant gain case these rays are constantly spaced in ⁇ , with about 8.5° between each ray, and from Fig. 4, that the spacing between the rays in the variable gain case increases with increasing ⁇ . So, in the variable gain case, a greater proportion of the scene is imaged towards the outer edge of the polar image. This is also shown in Figures 5 A and 5B, ray traced images reflected in a constant gain and variable gain mirror with the same range of elevations visible.
  • a mirror with two convex portions or a double mirror is required.
  • the radial profile of a double mirror is shown in Figure 8.
  • the mirror arrangement for panoramic stereo with variable gain mirrors will necessarily be different than for constant gain mirrors due to the variation of the mirror gain, .
  • the gain must vary in a constant fashion over the entire double mirror so that the constant pixel density theorem will hold over the entire image. If the minimum and maximum elevations viewed ( ⁇ and ⁇ ) are to be equal for both mirrors in the double mirror system, the range of reflected angles (V - ⁇ ) cannot be equal for the two mirrors.
  • the minimum and maximum angles of reflected rays captured by the camera over the entire mirror surface are known from camera geometry. Therefore the minimum ray reflected from the lower mirror ( ⁇ ) and the maximum ray reflected from the upper mirror ( ⁇ 2 ) are known. So, since (12) holds over the entire mirror, B ⁇ is constant, and from (14)
  • tan 2 ( ⁇ ,) tan 2 ( ⁇ ,) tan 2 ( ⁇ 2 ) + tan 2 ( ⁇ ,)
  • Figures 6A, 6B and 7 A, 7B show graphical and ray traced comparisons of constant and variable gain double mirror systems viewing the same scene.
  • the information available for range calculation are the image angles for a single object reflected in both mirrors, ⁇ , and ⁇ 2 as shown in Figure 8.
  • the two mirrors ⁇ j and ⁇ 2 form a reflective surface.
  • the differential equations (6) for the surfaces are known. In the calculations that follow only the lower mirror is examined as the results are identical for the upper mirror.
  • m R] the gradient of the reflected beam from the lower mirror to the camera and dy,/dx, is the gradient of the lower mirror profile at the reflection point.
  • the gradient of the mirror profile for the lower variable gain mirror is found as in the constant gain case, from dy. dy dx. dx ⁇ d ⁇ «_ ,
  • variable gain mirror profile i ⁇ + ⁇ + tan2 ( ⁇ )
  • Equation constants for the incident beam equations from (18) require the polar coordinates of the reflection points from each mirror, (r lt ⁇ ,) and (r 2 , ⁇ 2 ) . Since the variable gain mirror equations are not known exactly, r ; and r 2 must be found using a differential equation solver to find solutions to (26) at ⁇ ⁇ and ⁇ 2 .
  • a key disadvantage of single camera stereo panoramic systems is that since there are two images of the "same" scene, the pixels assigned to each image is half that for non stereo panoramic imaging and the two images do not share an equal number of pixels in constant gain schemes.
  • the panoramic stereo double mirror method typically causes the view of a scene in one radial direction to be compressed into around 1/4 the field of view of the camera.
  • a method to achieve panoramic stereo with less image compression is to use two cameras and two single curved mirror surfaces back to back, as shown in Fig. 9.
  • This method compresses the imaged scene into 1/2 the field of view of the camera, and indeed each image has an equal share of the total number of pixels available.
  • Fig. 9 An advantage of the scheme proposed in Fig. 9 is that the stereo cone can be symmetric about the horizon using two cameras with equal fields of view and the maximum and minimum angles of elevation reflected by the two mirrors being equal.
  • the angle covered by the stereo cone in this case is 2 ⁇ - ⁇ .
  • Fig.9 shows the general case where the maximum and minimum angles of elevations viewed by each camera need not be equal. The range of elevations must still be equal for the fields of view to be aligned.
  • the mirror families can be either constant gain or resolution invariant.
  • Fig. 10 shows a back to back design incorporating double mirrors.
  • the double mirror can also have a variable gain.
  • the advantage to this system is that the stereo cone from the back to back configuration combines with the stereo cones from the double mirror configuration to increase the total area imaged in stereo. In this configuration, the fields of view of each double mirror pair need not be aligned as in previous examples.
  • FIG. 11 An example of a forward looking mirror design is shown in Fig. 11.
  • a panoramic camera looking out from, say, a hemisphere, somewhat as an eye of a bird, or perhaps two such on either side of a "nose cone".
  • This configuration is termed forward looking because the camera faces towards the scene.
  • Either a constant or variable gain mirror (double or single) could be used for the curved mirror in the system.
  • the planar mirror is an annulus or circle interposed such that all rays reflected from the curved mirror are reflected into camera o positioned behind the curved mirror.
  • the dotted lines in Fig. 11 show where the reflected rays would converge if the planar mirror was removed and the dotted camera shows the camera o ' for an equivalent system without the planar mirror.
  • the planar mirror In order for the rays reflected by the planar mirror to converge at the new camera position, the planar mirror must be the perpendicular bisector of the line joining the old and new camera locations. Hence the distance between the camera locations is 2D where D is defined in Fig. 11 as the distance from either camera to the planar mirror.
  • the introduction of the planar mirror into the system does increase the possibility of alignment difficulties as the planar mirror must be perpendicular to the camera axis and also be positioned so as to reflect all rays from the curved mirror into the camera without occluding the view of the curved mirror.
  • the maximum value for D,D is when the maximum beam reflected from the mirror system (the D beam reflected at point b on the planar mirror) into camera o grazes the curved profile at c. In this case
  • D defines the minimum height for the mirror system, H .
  • the value for D needs to be slightly smaller to avoid occlusion, leading to a larger mirror system height.
  • the general equation for the height of the mirror system is
  • ⁇ must be greater than zero for camera o to be located behind the curved mirror. Also, ⁇ _ ⁇ if the minimum elevation ray ⁇ is not to be occluded by the planar mirror.
  • Fig. 12 shows a design that incorporates the ideas of Sections 2 and 3. It consists of two forward looking systems back to back, giving a design reminiscent of a eye mounted on a stalk, such as a crab's eye.
  • the "stalk" for this system would be hidden from view by the lower planar mirror.
  • portions are provided in the curved mirror to provide for reflection of rays from the curved surface to the camera by the plane mirrors.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Stereoscopic And Panoramic Photography (AREA)
  • Studio Devices (AREA)
  • Length Measuring Devices By Optical Means (AREA)
  • Closed-Circuit Television Systems (AREA)

Abstract

Un système d'imagerie panoramique comprend un dispositif d'imagerie présentant un plan d'image ainsi qu'un premier champ visuel, une première surface réfléchissante ayant au moins une partie symétrique circulairement convexe dans un sens radial, disposée dans le premier champ visuel pour fournir un second champ visuel panoramique élargi. Le profil de la partie convexe de chaque partie convexe procure un gain variant entre les champs visuels dans le sens radial pour limiter la variation de l'angle solide de vue dans le plan d'image du dispositif d'imagerie.
PCT/AU2000/000022 1999-01-15 2000-01-14 Imagerie panoramique invariante en resolution WO2000042470A1 (fr)

Priority Applications (3)

Application Number Priority Date Filing Date Title
AU24249/00A AU757227B2 (en) 1999-01-15 2000-01-14 Resolution invariant panoramic imaging
JP2000593986A JP2002535700A (ja) 1999-01-15 2000-01-14 解像力不変パノラマイメージング
EP00902499A EP1151349A1 (fr) 1999-01-15 2000-01-14 Imagerie panoramique invariante en resolution

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
AUPP8191 1999-01-15
AUPP8191A AUPP819199A0 (en) 1999-01-15 1999-01-15 Resolution invariant panoramic imaging

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WO2000042470A1 true WO2000042470A1 (fr) 2000-07-20

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WO (1) WO2000042470A1 (fr)

Cited By (5)

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Publication number Priority date Publication date Assignee Title
WO2002008817A2 (fr) * 2000-07-21 2002-01-31 Lee Scott Friend Dispositifs d'imagerie omnidirectionnels stereoscopiques
FR2826221A1 (fr) * 2001-05-11 2002-12-20 Immervision Internat Pte Ltd Procede d'obtention et d'affichage d'une image panoramique numerique a resolution variable
DE102005029612A1 (de) * 2005-06-23 2007-01-04 Hochschule Bremen Vorrichtung zum Erzeugen eines Panoramabildes
WO2012124275A1 (fr) * 2011-03-11 2012-09-20 Sony Corporation Appareil de traitement d'image, procédé de traitement d'image et programme
US10204398B2 (en) 2016-02-16 2019-02-12 6115187 Canada, Inc. Image distortion transformation method and apparatus

Families Citing this family (1)

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Publication number Priority date Publication date Assignee Title
JP4554954B2 (ja) * 2004-02-19 2010-09-29 康史 八木 全方位撮像システム

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US5627675A (en) * 1995-05-13 1997-05-06 Boeing North American Inc. Optics assembly for observing a panoramic scene

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US4449786A (en) * 1978-06-19 1984-05-22 Mccord Robert C Rearview mirror
US4549208A (en) * 1982-12-22 1985-10-22 Hitachi, Ltd. Picture processing apparatus
US4566763A (en) * 1983-02-08 1986-01-28 Budapesti Muszaki Egyetem Panoramic imaging block for three-dimensional space
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US5627675A (en) * 1995-05-13 1997-05-06 Boeing North American Inc. Optics assembly for observing a panoramic scene

Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2002008817A2 (fr) * 2000-07-21 2002-01-31 Lee Scott Friend Dispositifs d'imagerie omnidirectionnels stereoscopiques
WO2002008817A3 (fr) * 2000-07-21 2002-04-18 Lee Scott Friend Dispositifs d'imagerie omnidirectionnels stereoscopiques
FR2826221A1 (fr) * 2001-05-11 2002-12-20 Immervision Internat Pte Ltd Procede d'obtention et d'affichage d'une image panoramique numerique a resolution variable
WO2002093908A3 (fr) * 2001-05-11 2003-02-27 Immervision Internat Pte Ltd Procede de capture et d'affichage d'une image panoramique numerique a resolution variable
US6844990B2 (en) 2001-05-11 2005-01-18 6115187 Canada Inc. Method for capturing and displaying a variable resolution digital panoramic image
DE102005029612A1 (de) * 2005-06-23 2007-01-04 Hochschule Bremen Vorrichtung zum Erzeugen eines Panoramabildes
WO2012124275A1 (fr) * 2011-03-11 2012-09-20 Sony Corporation Appareil de traitement d'image, procédé de traitement d'image et programme
JP2012190299A (ja) * 2011-03-11 2012-10-04 Sony Corp 画像処理装置および方法、並びにプログラム
CN103443582A (zh) * 2011-03-11 2013-12-11 索尼公司 图像处理设备、图像处理方法和程序
EP2671045A1 (fr) * 2011-03-11 2013-12-11 Sony Corporation Appareil de traitement d'image, procédé de traitement d'image et programme
EP2671045A4 (fr) * 2011-03-11 2014-10-08 Sony Corp Appareil de traitement d'image, procédé de traitement d'image et programme
US10204398B2 (en) 2016-02-16 2019-02-12 6115187 Canada, Inc. Image distortion transformation method and apparatus
US10748243B2 (en) 2016-02-16 2020-08-18 Immervision, Inc. Image distortion transformation method and apparatus

Also Published As

Publication number Publication date
EP1151349A1 (fr) 2001-11-07
JP2002535700A (ja) 2002-10-22
AUPP819199A0 (en) 1999-02-11

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