程序代写 Field of view – cscodehelp代写

Field of view
FOV
Common FOV
O
One camera can only take an image of those locations within its field of view (FOV)
OL
OR
Computer Vision / Mid-Level Vision / Stereo and Depth
31
A stereo pair of cameras can find depth for those locations within the common FOV of the two cameras

Stereo: coplanar cameras
cFOV
cFOV
OLOR OLOR
Short baseline
• large common FOV • large depth error (changes in depth cause only small changes in disparity)
Long baseline
• small common FOV • small depth error
z= f Computer Vision / Mid-Level Vision / Stereo and Depth
B
d (changes in depth
cause larger changes in disparity)
32

Stereo: non-coplanar cameras
FOV
OL OR OL OR
Intersecting optical axes • large common FOV
• small depth error
Convergence angle θ (“vergence”)
Computer Vision / Mid-Level Vision / Stereo and Depth
33
Fixation point θ

Stereo: non-coplanar cameras
Disparity measured using angles instead of distance
Disparity = αL- αR
Disparity = zero at fixation point
Disparity = zero at all points on a curve where rays at equal angles intersect.
Curve with zero-disparity called the “horopter”
Location of horopter depends on vergence angle.
Fixation point
θ
Horopter
Computer Vision / Mid-Level Vision / Stereo and Depth
34
OL
OR
αL
αR

Stereo: non-coplanar cameras
Magnitude of disparity increases with the distance of objects from the horopter
(αL- αR) > 0 : outside of the horopter (αL- αR) < 0 : inside the horopter Need to be consistent with signs of angles, and order of subtraction. Fixation point θ Horopter Computer Vision / Mid-Level Vision / Stereo and Depth 35 OL OR αL αR Stereo: non-coplanar eyes Humans employ a non-coplanar imaging system. When point F is fixated: • The images of F fall on the foveas of each retina. D • The images of points on the horopter (e.g. H) fall an equal distance from the foveas of each retina. N • The images of points nearer than the horopter (e.g. N) are displaced outwards (“crossed” disparties) • The images of points more distant than the horopter (e.g. D) are displaced inwards (“uncrossed disparities) • The further the point from the H horopter, the greater the N left displacement. F D eye Computer Vision / Mid-Level Vision / Stereo and Depth F H right eye H D FN 36 Horopter Stereo: non-coplanar eyes Some cortical neurons are tuned to retinal disparity, and hence, can signal the depth of image points [see lecture 4]. left eye right eye disparity tuned neurons 2 0 -2 Computer Vision / Mid-Level Vision / Stereo and Depth 37 Epipolar geometry For coplanar cameras, corresponding points in the two images are on corresponding rows of each image. pl Ol pr P Computer Vision / Mid-Level Vision / Stereo and Depth 38 Or Epipolar Lines Epipolar geometry For non-coplanar cameras, corresponding points still occur on lines, but these are no longer horizontal lines. A point in the image plane of the left camera corresponds to a line in the image plane of the right camera (and vice versa). P pl Epipolar Lines pr Ol el er Or These lines which correspond to points in the other image are called epipolar lines. 2D search for correspondence can be reduced to a 1D search along the “epipolar” line. Computer Vision / Mid-Level Vision / Stereo and Depth 39 Epipolar geometry: terminology Baseline: the line through the camera projection centres Ol, Or Epipole: projection of the optic centre of one camera on the image plane of the other camera. The right (left) epipole er (el ) is the image of the left (right) camera projection centre Ol (Or) in the right (left) image plane. Equivalently, the epipoles are the intersection of the baseline with each image plane. P Computer Vision / Mid-Level Vision / Stereo and Depth 40 pl Epipoles pr Ol el er Or Baseline Epipolar geometry: terminology Epipolar plane: a plane going through a particular 3D point and the optic centres of both cameras. Epipolar lines: intersection of the epipolar plane (for a particular 3D point) and each image plane. All epipolar lines in the left image go through el and all epipolar lines in the right e image go through er. Ol P pl Epipolar Lines pr Conjugated epipolar lines: the epipolar lines generated by the same 3D point on the left and right image planes. Epipolar plane l e r Or Epipolar Constraint: Corresponding points must lie on conjugated epipolar lines. Computer Vision / Mid-Level Vision / Stereo and Depth 41 Rectification Epipolar lines can be made parallel to the rows of the image via a transform called rectification. Left Right Epipolar Lines Rectification warps both images so that all epipolar lines are horizontal. Computer Vision / Mid-Level Vision / Stereo and Depth 43 Stereo geometry: summary simple case P general case P yp yp pryr lzl xll z pr yr zr l lzlr xlO xrO lr T coplanar image planes (cameras translated along x-axis). epipolar lines are horizontal scan lines disparity measured in pixels disparity inversely proportional to depth Computer Vision / Mid-Level Vision / Stereo and Depth Ol xr Or T+R noncoplanar image planes (cameras related by a translation and rotation) epipolar lines are lines radiating from the epipolar point disparity measured using angles disparity increases with distance from horopter 44 Stereo geometry: summary simple case P general case P yp yp pryr lzl xll z l lzlr xlO xrO lr T Ol xr Or 1. triangulation (i.e. determining intersection of corresponding viewlines) 2. rectification of images and then treating as simple case Both require knowledge of intrinsic and extrinsic camera parameters. 45 depth = fB/d depth found by, either: Computer Vision / Mid-Level Vision / Stereo and Depth pr yr zr T+R