tailieunhanh - Structure from motion
Invite you to consult the lecture content "Structure from motion" below. Contents of lectures introduce to you the content: Structure from motion, structure from motion ambiguity, types of ambiguity,. Hopefully document content to meet the needs of learning, work effectively. | Structure from motion Multiple-view geometry questions Scene geometry (structure): Given 2D point matches in two or more images, where are the corresponding points in 3D? Correspondence (stereo matching): Given a point in just one image, how does it constrain the position of the corresponding point in another image? Camera geometry (motion): Given a set of corresponding points in two or more images, what are the camera matrices for these views? Structure from motion Given: m images of n fixed 3D points xij = Pi Xj , i = 1, , m, j = 1, , n Problem: estimate m projection matrices Pi and n 3D points Xj from the mn correspondences xij x1j x2j x3j Xj P1 P2 P3 Structure from motion ambiguity If we scale the entire scene by some factor k and, at the same time, scale the camera matrices by the factor of 1/k, the projections of the scene points in the image remain exactly the same: It is impossible to recover the absolute scale of the scene! Structure from motion . | Structure from motion Multiple-view geometry questions Scene geometry (structure): Given 2D point matches in two or more images, where are the corresponding points in 3D? Correspondence (stereo matching): Given a point in just one image, how does it constrain the position of the corresponding point in another image? Camera geometry (motion): Given a set of corresponding points in two or more images, what are the camera matrices for these views? Structure from motion Given: m images of n fixed 3D points xij = Pi Xj , i = 1, , m, j = 1, , n Problem: estimate m projection matrices Pi and n 3D points Xj from the mn correspondences xij x1j x2j x3j Xj P1 P2 P3 Structure from motion ambiguity If we scale the entire scene by some factor k and, at the same time, scale the camera matrices by the factor of 1/k, the projections of the scene points in the image remain exactly the same: It is impossible to recover the absolute scale of the scene! Structure from motion ambiguity If we scale the entire scene by some factor k and, at the same time, scale the camera matrices by the factor of 1/k, the projections of the scene points in the image remain exactly the same More generally: if we transform the scene using a transformation Q and apply the inverse transformation to the camera matrices, then the images do not change Types of ambiguity Projective 15dof Affine 12dof Similarity 7dof Euclidean 6dof Preserves intersection and tangency Preserves parallellism, volume ratios Preserves angles, ratios of length Preserves angles, lengths With no constraints on the camera calibration matrix or on the scene, we get a projective reconstruction Need additional information to upgrade the reconstruction to affine, similarity, or Euclidean Projective ambiguity Projective ambiguity Affine ambiguity Affine Affine ambiguity Similarity ambiguity Similarity ambiguity Structure from motion Let’s start with affine cameras (the math is easier)
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