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wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 outline toggle outline subsection 1 1 active stereo vision 2 applications 3 detailed definition toggle detailed definition subsection 3 1 image rectification 3 2 smoothness 4 information measure toggle information measure subsection 4 1 least squares information measure 4 2 information measure for stereoscopic images 5 methods of implementation 6 see also 7 references 8 external links toggle the table of contents computer stereo vision 4 languages français 日本語 한국어 українська edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia extraction of 3d data from digital images computer stereo vision is the extraction of three dimensional information from digital images such as those obtained by a ccd camera by comparing information about a scene from two vantage points 3d information can be extracted by examining the relative positions of objects in the two panels this is similar to the biological process of stereopsis outline edit in traditional stereoscopic vision two cameras displaced horizontally from one another are used to obtain two differing views on a scene in a manner similar to human binocular vision by comparing these two images the relative depth information can be obtained in the form of a disparity map which encodes the difference in horizontal coordinates of corresponding image points the values in this disparity map are inversely proportional to the scene depth at the corresponding pixel location for a human to compare the two images they must be superimposed in a stereoscopic device with the image from the right camera being shown to the observer s right eye and from the left one to the left eye in a computer vision system several pre processing steps are required 1 the image must first be undistorted such that barrel distortion and tangential distortion are removed this ensures that the observed image matches the projection of an ideal pinhole camera the image must be projected back to a common plane to allow comparison of the image pairs known as image rectification an information measure which compares the two images is minimized this gives the best estimate of the position of features in the two images and creates a disparity map optionally the received disparity map is projected into a 3d point cloud by utilising the cameras projective parameters the point cloud can be computed such that it provides measurements at a known scale active stereo vision edit active stereo vision is a form of stereo vision which actively employs a light such as a laser or a structured light to simplify the stereo matching problem the opposed term is passive stereo vision conventional structured light vision slv employs a structured light or laser and finds projector camera correspondences 2 3 conventional active stereo vision asv employs a structured light or laser however the stereo matching is performed only for camera camera correspondences in the same way as the passive stereo vision structured light stereo sls is a hybrid technique which utilizes both camera camera and projector camera correspondences 4 applications edit 3d stereo displays find many applications in entertainment information transfer and automated systems stereo vision is highly important in fields such as robotics to extract information about the relative position of 3d objects in the vicinity of autonomous systems other applications for robotics include object recognition 5 where depth information allows for the system to separate occluding image components such as one chair in front of another which the robot may otherwise not be able to distinguish as a separate object by any other criteria scientific applications for digital stereo vision include the extraction of information from aerial surveys for calculation of contour maps or even geometry extraction for 3d building mapping photogrammetric satellite mapping or calculation of 3d heliographical information such as obtained by the nasa stereo project detailed definition edit further information triangulation computer vision diagram describing relationship of image displacement to depth with stereoscopic images assuming flat co planar images a pixel records color at a position the position is identified by position in the grid of pixels x y and depth to the pixel z stereoscopic vision gives two images of the same scene from different positions in the adjacent diagram light from the point a is transmitted through the entry points of pinhole cameras at b and d onto image screens at e and h in the attached diagram the distance between the centers of the two camera lens is bd bc cd the triangles are similar acb and bfe acd and dgh therefore displacement d e f g h b f e f b f g h b f b f e f b f g h d g b f b c c d a c b f b d a c k z where displaystyle begin aligned text therefore displacement d ef gh bf frac ef bf frac gh bf bf frac ef bf frac gh dg bf frac bc cd ac bf frac bd ac frac k z text where end aligned k bd bf z ac is the distance from the camera plane to the object so assuming the cameras are level and image planes are flat on the same plane the displacement in the y axis between the same pixel in the two images is d k z displaystyle d frac k z where k is the distance between the two cameras times the distance from the lens to the image the depth component in the two images are z 1 displaystyle z_ 1 and z 2 displaystyle z_ 2 given by z 2 x y min v v z 1 x y k z 1 x y displaystyle z_ 2 x y min left v v z_ 1 x y frac k z_ 1 x y right z 1 x y min v v z 2 x y k z 2 x y displaystyle z_ 1 x y min left v v z_ 2 x y frac k z_ 2 x y right these formulas allow for the occlusion of voxels seen in one image on the surface of the object by closer voxels seen in the other image on the surface of the object image rectification edit where the image planes are not co planar image rectification is required to adjust the images as if they were co planar this may be achieved by a linear transformation the images may also need rectification to make each image equivalent to the image taken from a pinhole camera projecting to a flat plane smoothness edit smoothness is a measure of the similarity of colors given the assumption that a distinct object has a small number of colors similarly colored pixels are more likely to belong to a single object than to multiple objects the method described above for evaluating smoothness is based on information theory and an assumption that the influence of the color of a voxel influences the color of nearby voxels according to the normal distribution on the distance between points the model is based on approximate assumptions about the world another method based on prior assumptions of smoothness is auto correlation smoothness is a property of the world rather than an intrinsic property of an image an image comprising random dots would have no smoothness and inferences about neighboring points would be useless in principle smoothness as with other properties of the world should be learned this appears to be what the human vision system does citation needed information measure edit least squares information measure edit the normal distribution is p x μ σ 1 σ 2 π e x μ 2 2 σ 2 displaystyle p x mu sigma frac 1 sigma sqrt 2 pi e frac x mu 2 2 sigma 2 probability is related to information content described by message length l p x 2 l x displaystyle p x 2 l x l x log 2 p x displaystyle l x log _ 2 p x so l x μ σ log 2 σ 2 π x μ 2 2 σ 2 log 2 e displaystyle l x mu sigma log _ 2 sigma sqrt 2 pi frac x mu 2 2 sigma 2 log _ 2 e for the purposes of comparing stereoscopic images only the relative message length matters based on this the information measure i called the sum of squares of differences ssd is i x μ σ x μ 2 σ 2 displaystyle i x mu sigma frac x mu 2 sigma 2 where l x μ σ log 2 σ 2 π i x μ σ log 2 e 2 displaystyle l x mu sigma log _ 2 sigma sqrt 2 pi i x mu sigma frac log _ 2 e 2 because of the cost in processing time of squaring numbers in ssd many implementations use sum of absolute difference sad as the basis for computing the information measure other methods use normalized cross correlation ncc information measure for stereoscopic images edit the least squares measure may be used to measure the information content of the stereoscopic images 6 given depths at each point z x y displaystyle z x y firstly the information needed to express one image in terms of the other is derived this is called i m displaystyle i_ m a color difference function should be used to fairly measure the difference between colors the color difference function is written cd in the following the measure of the information needed to record the color matching between the two images is i m z 1 z 2 1 σ m 2 x y cd color 1 x y k z 1 x y color 2 x y 2 displaystyle i_ m z_ 1 z_ 2 frac 1 sigma _ m 2 sum _ x y operatorname cd operatorname color _ 1 x y frac k z_ 1 x y operatorname color _ 2 x y 2 an assumption is made about the smoothness of the image assume that two pixels are more likely to be the same color the closer the voxels they represent are this measure is intended to favor colors that are similar being grouped at the same depth for example if an object in front occludes an area of sky behind the measure of smoothness favors the blue pixels all being grouped together at the same depth the total measure of smoothness uses the distance between voxels as an estimate of the expected standard deviation of the color difference i s z 1 z 2 1 2 σ h 2 i 1 2 x 1 y 1 x 2 y 2 cd color i x 1 y 1 color i x 2 y 2 2 x 1 x 2 2 y 1 y 2 2 z i x 1 y 1 z i x 2 y 2 2 displaystyle i_ s z_ 1 z_ 2 frac 1 2 sigma _ h 2 sum _ i 1 2 sum _ x_ 1 y_ 1 sum _ x_ 2 y_ 2 frac operatorname cd operatorname color _ i x_ 1 y_ 1 operatorname color _ i x_ 2 y_ 2 2 x_ 1 x_ 2 2 y_ 1 y_ 2 2 z_ i x_ 1 y_ 1 z_ i x_ 2 y_ 2 2 the total information content is then the sum i t z 1 z 2 i m z 1 z 2 i s z 1 z 2 displaystyle i_ t z_ 1 z_ 2 i_ m z_ 1 z_ 2 i_ s z_ 1 z_ 2 the z component of each pixel must be chosen to give the minimum value for the information content this will give the most likely depths at each pixel the minimum total information measure is i min min i i i t z 1 z 2 displaystyle i_ operatorname min min i i i_ t z_ 1 z_ 2 the depth functions for the left and right images are the pair z 1 z 2 z 1 z 2 i t z 1 z 2 i min displaystyle z_ 1 z_ 2 in z_ 1 z_ 2 i_ t z_ 1 z_ 2 i_ operatorname min methods of implementation edit the minimization problem is np complete this means a general solution to this problem will take a long time to reach however methods exist for computers based on heuristics that approximate the result in a reasonable amount of time also methods exist based on neural networks 7 efficient implementation of stereoscopic vision is an area of active research see also edit 3d reconstruction from multiple images 3d scanner autostereoscopy computer vision epipolar geometry semi global matching structure from motion stereo camera stereophotogrammetry stereopsis stereoscopic depth rendition stixel trifocal tensor for trifocal stereoscopy using three images instead of two references edit bradski gary kaehler adrian learning opencv computer vision with the opencv library o reilly je changsoo lee sang wook park rae hong 2004 high contrast color stripe pattern for rapid structured light range imaging computer vision eccv 2004 lecture notes in computer science vol 3021 pp 95 107 arxiv 1508 04981 doi 10 1007 978 3 540 24670 1_8 isbn 978 3 540 21984 2 s2cid 13277591 je changsoo lee sang wook park rae hong 2012 colour stripe permutation pattern for rapid structured light range imaging optics communications 285 9 2320 2331 bibcode 2012optco 285 2320j doi 10 1016 j optcom 2012 01 025 jang wonkwi je changsoo seo yongduek lee sang wook 2013 structured light stereo comparative analysis and integration of structured light and active stereo for measuring dynamic shape optics and lasers in engineering 51 11 1255 1264 bibcode 2013optle 51 1255j doi 10 1016 j optlaseng 2013 05 001 sumi yasushi kawai yoshihiro yoshimi takashi tomita fumiaki 2002 3d object recognition in cluttered environments by segment based stereo vision international journal of computer vision 46 1 5 23 doi 10 1023 a 1013240031067 s2cid 22926546 lazaros nalpantidis sirakoulis georgios christou gasteratos1 antonios 2008 review of stereo vision algorithms from software to hardware international journal of optomechatronics 2 4 435 462 doi 10 1080 15599610802438680 s2cid 18115413 cite journal cs1 maint numeric names authors list link wang jung hua hsiao chih ping 1999 on disparity matching in stereo vision via a neural network framework proc natl sci counc roc a 23 5 665 678 citeseerx 10 1 1 105 9067 cite journal cite uses deprecated parameter citeseerx help external links edit stereo geometry by k konolige archived here tutorial on uncalibrated stereo vision learn about stereo vision with matlab stereo vision and rover navigation software for planetary exploration v t e computer vision categories datasets digital geometry commercial systems feature detection geometry image sensor technology learning morphology motion analysis noise reduction techniques recognition and categorization research infrastructure researchers segmentation software technologies computer stereo vision motion capture object recognition 3d object recognition applications 3d reconstruction 3d reconstruction from multiple images 2d to 3d conversion adop gaussian splatting neural radiance field shape from focus simultaneous localization and mapping structure from motion trilinear point splatting view synthesis visual hull 4d reconstruction free viewpoint television volumetric capture 3d pose estimation activity recognition audio visual speech recognition automatic image annotation automatic number plate recognition automated species identification augmented reality bioimage informatics bin picking blob detection computer aided diagnosis content based image retrieval reverse image search eye tracking face recognition foreground detection gesture recognition image denoising image restoration landmark detection medical image computing object detection moving object detection pedestrian detection small object detection optical character recognition pose tracking remote sensing robotic mapping autonomous vehicles video browsing video content analysis video motion analysis video surveillance video synopsis video tracking main 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