WO1996034365A1 - Appareil et procede pour recreer et manipuler un objet en 3d en fonction d'une projection en 2d de celui-ci - Google Patents

Appareil et procede pour recreer et manipuler un objet en 3d en fonction d'une projection en 2d de celui-ci Download PDF

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Publication number
WO1996034365A1
WO1996034365A1 PCT/US1996/005697 US9605697W WO9634365A1 WO 1996034365 A1 WO1996034365 A1 WO 1996034365A1 US 9605697 W US9605697 W US 9605697W WO 9634365 A1 WO9634365 A1 WO 9634365A1
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WO
WIPO (PCT)
Prior art keywords
views
trilinear
generating
scene
employing
Prior art date
Application number
PCT/US1996/005697
Other languages
English (en)
Other versions
WO1996034365A9 (fr
Inventor
Amnon Shashua
Original Assignee
Cognitens Ltd.
Cohen, Julian, H.
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
Priority claimed from IL11349695A external-priority patent/IL113496A/xx
Application filed by Cognitens Ltd., Cohen, Julian, H. filed Critical Cognitens Ltd.
Priority to JP8532665A priority Critical patent/JPH11504452A/ja
Priority to EP96913833A priority patent/EP0832471A4/fr
Priority to AU56674/96A priority patent/AU5667496A/en
Publication of WO1996034365A1 publication Critical patent/WO1996034365A1/fr
Publication of WO1996034365A9 publication Critical patent/WO1996034365A9/fr

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Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T15/00—3D [Three Dimensional] image rendering
    • G06T15/10—Geometric effects
    • G06T15/20—Perspective computation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/50—Depth or shape recovery
    • G06T7/55—Depth or shape recovery from multiple images
    • G06T7/593—Depth or shape recovery from multiple images from stereo images
    • G06T7/596—Depth or shape recovery from multiple images from stereo images from three or more stereo images
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10004—Still image; Photographic image
    • G06T2207/10012—Stereo images
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10032—Satellite or aerial image; Remote sensing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30181—Earth observation

Definitions

  • the present invention also seeks to provide improved apparatus and methods for processing 2D proj ections of 3D obj ects .
  • the step of providing may , for example , comprise scanning in the f irst and second reference images .
  • the step of employing may , for example , include the step of generating a set of first , second and third corresponding locations in the f irst reference view , second reference view and novel view , respectively .
  • the step of providing includes scanning in the first and second reference images .
  • 3D scene reconstruction apparatus for generating a 3D representation of a 3D scene from first , second and third views thereof , the apparatus including appparatus for providing f irst , second and third views of a 3D scene , a trilinear tensor generator operative to employ geometric information regarding the f irst , second and third views to generate a trilinear tensor representing the geometric relationship between the f irst , second and third views , and a 3D scene representation generator operative to generate a 3D representation of the 3D scene from the tril inear tensor .
  • a ij and b jk are elements of matrices A and B respectively and v i ' and v i " are elements of vectors v' and v" respectively, wherein the matrices and vectors together describe camera parameters of three views of the 3D object, and employing the array to generate information regarding the 3D object.
  • a method for reconstructing a 3D object from at least one and preferably three 2D projections thereof including providing at least one and preferably three 2D projections of a 3D object, generating an array of numbers described by:
  • the at least one and preferably three 2D projections includes at least one aerial photograph.
  • the 3D object includes a nonexistent object.
  • Fig. 6 is a simplified functional block diagram of 3D scene reconstruction apparatus, constructed and operative in accordance with a preferred embodiment of the present invention, which is operative to generate a 3D representation of a 3D scene from at least three views thereof;
  • Fig. 12 is a simplified block diagram illustration of a preferred method and apparatus for generating a digital terrain map.
  • a pin-hole camera like 35mm still camera or Video recorder, produces a two-dimensional projection (2D) of the viewed three-dimensional (3D) world.
  • the resulting image can be analyzed on a geometric and photometric level.
  • the geometric level means the geometric relation between the locations of features (points, lines) in 3D and their respective location in the 2D image.
  • the photometric level means the radiometric (reflectance properties of the surface, the spectral properties of the light sources illuminating the scene, etc.) relation between the scene and the luminosity (pixel grey values) in the image.
  • ⁇ rs , b ⁇ s are the elements of A, B, and v r ' , v r " are the elements of v', v", is referred to as the "trilinear tensor" .
  • These numbers are invariant to the particular projective representation of the 3D and 2D worlds, i.e., they are intrinsic to the three views (this is one of the general properties of tensors that they do not depend on the choice of basis for representation).
  • a corresponding triplet p, p', p" satisfies a number of trilinear relationships.
  • ⁇ ijk is a set of scalars
  • a ij . is a set of 9 vectors (k varies while i,j remain fixed):
  • ⁇ i .. is a set of 3 matrices ( ⁇ 1 .., ⁇ 2 .. and ⁇ 3 ..), and so forth.
  • a preferred implementation of units 50 and 60 is described, in "C" computer language form, in Appendix A.
  • a preferred implementation of unit 50 is described from page 1 of Appendix A until toward the end of page 4 thereof.
  • a preferred implementation of unit 60 is described from the end of page 4 of Appendix A until the middle of page 8. Subroutines and statistical procedures which are useful in understanding the above material appear from page 8 of Appendix A onward.
  • Synthetic images may then be generated for positions other than the 200 above-mentioned positions.
  • a desired position may be indicated by a user, e.g. by means of a joystick.
  • the apparatus of the present invention may be used to generate a synthetic image for that position.
  • Conventional driving simulation games employ synthetic backgrounds, however, the present invention may be employed to provide a driving simulation game with a real background.
  • an array of at least 3, and preferably 5 - 10 cameras is moved within a desired scene such that substantially the entirety of the scenes can be captured by the camera array from at least 3 and preferably more different perspectives.
  • the scene may be captured from each of approximately 1000 positions of the camera array.
  • New views are then generated, in accordance with the present invention, in order to accomodate a user's need for new views as indicated, e.g. by a joystick.
  • Theorem 3 is an obvious corollary of Theorem 1 but contains a significant practical aspect. It is shown that if the views ⁇ 1 , ⁇ 2 are obtained by parallel projection, then F reduces to a special bilinear form— or. equivalently. that any perspective view ⁇ can be obtained by a rat ional linear function of two orthographic views. The reduction to a bilinear form implies that simpler recognition schemes are possible if the two reference views (model views) stored in memory are orthographic.
  • the coefficient k is independent of ⁇ 2 , i. e. , is invariant to the choice of the second view.
  • E 1 ⁇ PGL 3 be the homography from ⁇ 1 to ⁇ 2
  • E 2 ⁇ PGL 3 the homography from ⁇ 2 to ⁇ 1 . Then with proper scaling of E 1 and E 2 we have
  • Theorem 2 There exists nine distinct trilinear forms of the type described in Theorem 1 of which at most four are linearly independent. The coefficients of the four trilinear forms can be recovered linearly with seven corresponding points across the three views.
  • a bilinear function of three views has two advantages over the general trilinear function. First, as mentioned above, only five corresponding points (instead of seven) across three views are required for solving for the coefficients. Second, the lower the degree of the algebraic function, the less sensitive the solution may be in the presence of errors in measuring correspondences. In other words, it is likely (though not necessary) that the higher order terms, such as the term x"x'x in Equation 3, will have a higher contribution to the overall error sensitivity of the system.
  • the trilinear method requires at least seven corresponding points across the three views ( we need 26 equation, and seven points provide 28 equations), whereas epipolar intersection can be done (in principle) with eight points.
  • the question we are about to address is what is t he number of points that are required in practice (due to errors in correspondence, lens distortions and other effects that are not adequately modeled by the pin-hole camera model ) t o achieve reasonable performance?
  • the trilinear result was first applied with the minimal number of points (seven) for solving for the coefficients, and then applied with 8,9, and 10 points using a linear least-squares solution ( note that in general, better solutions may be obtained by using SVD or Jacobi methods instead of linear least-squares, but that was not attempted here).
  • Re-projection techniques provide a short-cut for image rendering. Given two fully rendered views of some 3D object, other views (again ignoring self-occlusions) can be rendered by simply "combining" the reference views. Again, the number of corresponding points is less of a concern here.
  • the present invention has very broad applications and specifically is applicable in all fields in which 3D from 2D techniques are known to be useful.
  • Applications of the present invention include at least the following: photogrammetry applications comprising map making from aerial and satellite photographs and coordinate measurements in aerospace and shipyard assembly plants, coordinate measurements of industrial parts (CMM) , automated optical based inspection of industrial parts, robotic cell alignment, robotic trajectory identification, 3D robotic feedback, 3D modelling of scenes, 3D modelling of objects, reverse engineering, and 3D digitizing.
  • Programs generated from the listing of Appendix B may be loaded into Maple2 using the OPEN FILE command.
  • the subroutines may be run by bringing the cursor to the row on which appears the WITH (LINALG) command.
  • EVALN PCOMP
  • the system then prints on the screen a comparison between the given 3D world and the reconstructed 3D world .
  • Appendix B is also useful in implementing the image transfer apparatus and method shown and described herein .
  • the image transfer embodiment may , for example , be based on the listing of Appendix B used in conj unction with Equations 3 and 4 of the above section entitled Algebraic Function for Recognition .

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Computer Graphics (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Computing Systems (AREA)
  • Software Systems (AREA)
  • Image Processing (AREA)
  • Length Measuring Devices By Optical Means (AREA)
  • Processing Or Creating Images (AREA)

Abstract

Procédé de génération d'informations concernant un objet en 3D à partir d'au moins une projection en 2D de ce dernier. Le procédé consiste à produire au moins une projection en 2D (40) d'un objet en 3D, à générer un groupe de nombre (50, 60) représentés par: aijk = vi'bik - vj''ajk(i,j,k = 1,2,3), ajk et bjk étant respectivement des éléments des matrices A et B, vi' ainsi que vi'' étant respectivement des éléments des vecteurs v' et v''. Les matrices (50) et les vecteurs (60) décrivant ensemble des paramètres de caméra de trois vues (102) de l'objet en 3D et utilisant ledit groupe pour générer des informations concernant l'objet en 3D (70).
PCT/US1996/005697 1995-04-25 1996-04-24 Appareil et procede pour recreer et manipuler un objet en 3d en fonction d'une projection en 2d de celui-ci WO1996034365A1 (fr)

Priority Applications (3)

Application Number Priority Date Filing Date Title
JP8532665A JPH11504452A (ja) 1995-04-25 1996-04-24 ２次元投影図に基づいて３次元の対象物を再現し、取り扱うための装置と方法
EP96913833A EP0832471A4 (fr) 1995-04-25 1996-04-24 Appareil et procede pour recreer et manipuler un objet en 3d en fonction d'une projection en 2d de celui-ci
AU56674/96A AU5667496A (en) 1995-04-25 1996-04-24 Apparatus and method for recreating and manipulating a 3D object based on a 2D projection thereof

Applications Claiming Priority (4)

Application Number Priority Date Filing Date Title
IL113496 1995-04-25
IL11349695A IL113496A (en) 1995-04-25 1995-04-25 Apparatus and method for recreating and manipulating a 3d object based on a 2d projection thereof
US08/497,224 1995-06-30
US08/497,224 US5821943A (en) 1995-04-25 1995-06-30 Apparatus and method for recreating and manipulating a 3D object based on a 2D projection thereof

Publications (2)

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WO1996034365A1 true WO1996034365A1 (fr) 1996-10-31
WO1996034365A9 WO1996034365A9 (fr) 1996-12-27

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EP (1) EP0832471A4 (fr)
JP (1) JPH11504452A (fr)
CN (1) CN1198230A (fr)
AU (1) AU5667496A (fr)
CA (1) CA2219314A1 (fr)
WO (1) WO1996034365A1 (fr)

Cited By (13)

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Publication number Priority date Publication date Assignee Title
WO2000002162A1 (fr) * 1998-06-30 2000-01-13 Siemens Aktiengesellschaft Dispositif et procede pour la realisation d'un modele d'installation virtuel
EP1016029A2 (fr) * 1996-12-15 2000-07-05 Cognitens, Ltd Appareil et procede de reconstruction geometrique de surface tridimensionnelle
GB2338858B (en) * 1997-04-04 2000-12-27 Isis Innovation Microscopy imaging apparatus and method
US6201541B1 (en) * 1997-12-11 2001-03-13 Cognitens, Ltd. System and method for “Stitching” a plurality of reconstructions of three-dimensional surface features of object(s) in a scene defined relative to respective coordinate systems to relate them to a common coordinate system
WO2003012368A1 (fr) 2001-07-30 2003-02-13 Topcon Corporation Appareil de mesure d'une forme superficielle, procede de mesure d'une forme superficielle et appareil graphique destine a l'etat superficiel
US7054793B2 (en) 1998-07-22 2006-05-30 Siemens Aktiengesellschaft Device and method for generating a virtual model of an installation
US8917169B2 (en) 1993-02-26 2014-12-23 Magna Electronics Inc. Vehicular vision system
US8993951B2 (en) 1996-03-25 2015-03-31 Magna Electronics Inc. Driver assistance system for a vehicle
US9008369B2 (en) 2004-04-15 2015-04-14 Magna Electronics Inc. Vision system for vehicle
US9436880B2 (en) 1999-08-12 2016-09-06 Magna Electronics Inc. Vehicle vision system
US9555803B2 (en) 2002-05-03 2017-01-31 Magna Electronics Inc. Driver assistance system for vehicle
US10071676B2 (en) 2006-08-11 2018-09-11 Magna Electronics Inc. Vision system for vehicle
US11963868B2 (en) 2020-06-01 2024-04-23 Ast Products, Inc. Double-sided aspheric diffractive multifocal lens, manufacture, and uses thereof

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EP1661116A4 (fr) * 2003-07-29 2010-12-01 Pixar Procede de projection de peinture ameliore et dispositif correspondant
CN104596484A (zh) * 2015-01-30 2015-05-06 黄河水利委员会黄河水利科学研究院 一种黄河凌汛期流凌密度测量方法
KR101865112B1 (ko) 2017-03-07 2018-07-13 광주과학기술원 외관 재질 모델링을 포함하는 3차원 복원 장치 및 그 방법

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Cited By (41)

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Publication number Priority date Publication date Assignee Title
US8917169B2 (en) 1993-02-26 2014-12-23 Magna Electronics Inc. Vehicular vision system
US8993951B2 (en) 1996-03-25 2015-03-31 Magna Electronics Inc. Driver assistance system for a vehicle
EP1016029A2 (fr) * 1996-12-15 2000-07-05 Cognitens, Ltd Appareil et procede de reconstruction geometrique de surface tridimensionnelle
EP1016029A4 (fr) * 1996-12-15 2006-05-03 Cognitens Ltd Appareil et procede de reconstruction geometrique de surface tridimensionnelle
GB2338858B (en) * 1997-04-04 2000-12-27 Isis Innovation Microscopy imaging apparatus and method
US6376818B1 (en) 1997-04-04 2002-04-23 Isis Innovation Limited Microscopy imaging apparatus and method
US6201541B1 (en) * 1997-12-11 2001-03-13 Cognitens, Ltd. System and method for “Stitching” a plurality of reconstructions of three-dimensional surface features of object(s) in a scene defined relative to respective coordinate systems to relate them to a common coordinate system
WO2000002162A1 (fr) * 1998-06-30 2000-01-13 Siemens Aktiengesellschaft Dispositif et procede pour la realisation d'un modele d'installation virtuel
US7054793B2 (en) 1998-07-22 2006-05-30 Siemens Aktiengesellschaft Device and method for generating a virtual model of an installation
US9436880B2 (en) 1999-08-12 2016-09-06 Magna Electronics Inc. Vehicle vision system
EP1422495A1 (fr) * 2001-07-30 2004-05-26 Topcon Corporation Appareil de mesure d'une forme superficielle, procede de mesure d'une forme superficielle et appareil graphique destine a l'etat superficiel
EP1422495A4 (fr) * 2001-07-30 2009-06-03 Topcon Corp Appareil de mesure d'une forme superficielle, procede de mesure d'une forme superficielle et appareil graphique destine a l'etat superficiel
WO2003012368A1 (fr) 2001-07-30 2003-02-13 Topcon Corporation Appareil de mesure d'une forme superficielle, procede de mesure d'une forme superficielle et appareil graphique destine a l'etat superficiel
US9834216B2 (en) 2002-05-03 2017-12-05 Magna Electronics Inc. Vehicular control system using cameras and radar sensor
US10118618B2 (en) 2002-05-03 2018-11-06 Magna Electronics Inc. Vehicular control system using cameras and radar sensor
US11203340B2 (en) 2002-05-03 2021-12-21 Magna Electronics Inc. Vehicular vision system using side-viewing camera
US9555803B2 (en) 2002-05-03 2017-01-31 Magna Electronics Inc. Driver assistance system for vehicle
US10683008B2 (en) 2002-05-03 2020-06-16 Magna Electronics Inc. Vehicular driving assist system using forward-viewing camera
US9643605B2 (en) 2002-05-03 2017-05-09 Magna Electronics Inc. Vision system for vehicle
US10351135B2 (en) 2002-05-03 2019-07-16 Magna Electronics Inc. Vehicular control system using cameras and radar sensor
US10187615B1 (en) 2004-04-15 2019-01-22 Magna Electronics Inc. Vehicular control system
US10735695B2 (en) 2004-04-15 2020-08-04 Magna Electronics Inc. Vehicular control system with traffic lane detection
US10015452B1 (en) 2004-04-15 2018-07-03 Magna Electronics Inc. Vehicular control system
US11847836B2 (en) 2004-04-15 2023-12-19 Magna Electronics Inc. Vehicular control system with road curvature determination
US10110860B1 (en) 2004-04-15 2018-10-23 Magna Electronics Inc. Vehicular control system
US9008369B2 (en) 2004-04-15 2015-04-14 Magna Electronics Inc. Vision system for vehicle
US9428192B2 (en) 2004-04-15 2016-08-30 Magna Electronics Inc. Vision system for vehicle
US10306190B1 (en) 2004-04-15 2019-05-28 Magna Electronics Inc. Vehicular control system
US9736435B2 (en) 2004-04-15 2017-08-15 Magna Electronics Inc. Vision system for vehicle
US10462426B2 (en) 2004-04-15 2019-10-29 Magna Electronics Inc. Vehicular control system
US9609289B2 (en) 2004-04-15 2017-03-28 Magna Electronics Inc. Vision system for vehicle
US9948904B2 (en) 2004-04-15 2018-04-17 Magna Electronics Inc. Vision system for vehicle
US11503253B2 (en) 2004-04-15 2022-11-15 Magna Electronics Inc. Vehicular control system with traffic lane detection
US9191634B2 (en) 2004-04-15 2015-11-17 Magna Electronics Inc. Vision system for vehicle
US11148583B2 (en) 2006-08-11 2021-10-19 Magna Electronics Inc. Vehicular forward viewing image capture system
US11396257B2 (en) 2006-08-11 2022-07-26 Magna Electronics Inc. Vehicular forward viewing image capture system
US10787116B2 (en) 2006-08-11 2020-09-29 Magna Electronics Inc. Adaptive forward lighting system for vehicle comprising a control that adjusts the headlamp beam in response to processing of image data captured by a camera
US11623559B2 (en) 2006-08-11 2023-04-11 Magna Electronics Inc. Vehicular forward viewing image capture system
US10071676B2 (en) 2006-08-11 2018-09-11 Magna Electronics Inc. Vision system for vehicle
US11951900B2 (en) 2006-08-11 2024-04-09 Magna Electronics Inc. Vehicular forward viewing image capture system
US11963868B2 (en) 2020-06-01 2024-04-23 Ast Products, Inc. Double-sided aspheric diffractive multifocal lens, manufacture, and uses thereof

Also Published As

Publication number Publication date
JPH11504452A (ja) 1999-04-20
AU5667496A (en) 1996-11-18
EP0832471A1 (fr) 1998-04-01
EP0832471A4 (fr) 2000-05-10
CA2219314A1 (fr) 1996-10-31
CN1198230A (zh) 1998-11-04

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