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Displacement Relief Note: nominal scale is the same everywhere in the image CE 503 Photogrammetry I Fall 2006 Purdue University Frame Geometry CE 503 Photogrammetry I Fall 2006 Purdue University Frame Geometry with Lens for Large Aperture CE 503 Photogrammetry I Fall 2006 Purdue University Relief Displacement Layout of vertically extended objects within an image Relief displacement as found in frame imagery, entire image captured at same instant, relief displacement is always radial with respect to the nadir point Relief displacement as found in pushbroom imagery, the image is built up over time by the platform motion, relief displacement only exists within a line. It is still radial with respect to the nadir point, but there is a different nadir point for every line. Therefore the only component of relief displacement is cross-track, there is no along-track component. (platform motion is up/down) CE 503 Photogrammetry I Fall 2006 Purdue University Relief Displacement for Nadir Imagery Ideal geometry: nadir imagery, flat terrain r: radial distance from nadir point/principal point to top of object f dr r By similarity of small triangle at lower right and the large triangle: h dR = H R H By proportionality of segments when parallel lines cut a bundle of rays: dr dR = r R h dR R CE 503 Photogrammetry I Fall 2006 Purdue University Rearrange for classic relief displacement formula: h= r H r Note relief displacement in Quickbird (Satellite Camera) image. With narrow field of view, displacement is effectively the same throughout the field of view, and depends on the tilt or off-nadir view angle CE 503 Photogrammetry I Fall 2006 Purdue University Parallax: apparent change in position due to change in view location (sometimes called disparity) Base = B f xr Bp = Hf B H= f p xl xr H parallax = p = xl xr Object distance ~ 1/p => big distance : small parallax => small distance : big parallax dp B f B = fBH 2 = = ( scale) dH H H H => Rate of change of parallax with respect to distance ~ scale and B/H CE 503 Photogrammetry I Fall 2006 Purdue University L R R Near point (top tank) of makes a larger excursion between the left and right exposure, compared to the base of the tank (larger parallax or larger disparity). This disparity can be processed by our eyes to sense depth. A stereo cursor can be placed on an object to measure 3D coordinates delineate 3D features. If image B/H is greater than our eye s b/h, then we sense vertical exaggeration. This changes the appearance, but does not hurt measurement accuracy (in fact it helps). CE 503 Photogrammetry I Fall 2006 Purdue University Anaglyph Stereo of Mars scene shows greater disparity or parallax in foreground and less in the background or far distance CE 503 Photogrammetry I Fall 2006 Purdue University Wide angle and given overlap yields large B/H ratio Narrow angle and same overlap yields small B/H ratio Can compensate for narrow angle camera by introducing strong convergence angle thus restoring favorable B/H ratio CE 503 Photogrammetry I Fall 2006 Purdue University High frame rate motion imagery = short baseline or small B/H (between adjacent images) Conventional aerial imagery = long baseline or large B/H Correspondence is easy, since small displacements and parallaxes between adjacent images, for point tracking or optical flow, but determination of heights is weak (unless you extend over many frames) Correspondence can be a challenge if large parallaxes, but determination of heights is strong CE 503 Photogrammetry I Fall 2006 Purdue University (XL,ZL) SPOT Off-Nadir Relief Displacement Focal length = 83231 pix m12 X X L m x = k 11 f m21 m22 Z Z L x m ( X X L ) + m12 ( Z Z L ) = 11 f m21 ( X X L ) + m22 ( Z Z L ) x= f m11 ( X X L ) + m12 ( Z Z L ) m21 ( X X L ) + m22 ( Z Z L ) m12 cos 1 sin 1 = m22 sin 1 cos 1 H=822 km dx 2 1 3 m M = 11 m21 For h=300m, theta-2=2 deg, we have the following values for theta-1 and dx: h dx 10 deg 6.2 pix 20 deg 10.6 pix 27 deg 13.0 pix Relief displacment for offnadir SPOT is significant 1 X CE 503 Photogrammetry I Fall 2006 Purdue University

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