TY - JOUR
T1 - Shape from specular flow
AU - Adato, Yair
AU - Vasilyev, Yuriy
AU - Zickler, T.
AU - Ben-Shahar, Ohad
N1 - Funding Information:
This research is supported by the Israel Science Foundation under grant no. 1245/08 and the US National Science Foundation (NSF) under grant no. IIS-0712956. Ohad Ben-Shahar and Yair Adato also thank the generous support of the Frankel Fund and the Paul Ivanier Robotics Center at Ben-Gurion University. Additional funding for Todd Zickler and Yriy Vasilyev was provided by the NSF under CAREER Award IIS-0546408.
PY - 2010/8/24
Y1 - 2010/8/24
N2 - An image of a specular (mirror-like) object is nothing but a distorted reflection of its environment. When the environment is unknown, reconstructing shape from such an image can be very difficult. This reconstruction task can be made tractable when, instead of a single image, one observes relative motion between the specular object and its environment, and therefore, a motion fieldor specular flowin the image plane. In this paper, we study the shape from specular flow problem and show that observable specular flow is directly related to surface shape through a nonlinear partial differential equation. This equation has the key property of depending only on the relative motion of the environment while being independent of its content. We take first steps toward understanding and exploiting this PDE, and we examine its qualitative properties in relation to shape geometry. We analyze several cases in which the surface shape can be recovered in closed form, and we show that, under certain conditions, specular shape can be reconstructed when both the relative motion and the content of the environment are unknown. We discuss numerical issues related to the proposed reconstruction algorithms, and we validate our findings using both real and synthetic data.
AB - An image of a specular (mirror-like) object is nothing but a distorted reflection of its environment. When the environment is unknown, reconstructing shape from such an image can be very difficult. This reconstruction task can be made tractable when, instead of a single image, one observes relative motion between the specular object and its environment, and therefore, a motion fieldor specular flowin the image plane. In this paper, we study the shape from specular flow problem and show that observable specular flow is directly related to surface shape through a nonlinear partial differential equation. This equation has the key property of depending only on the relative motion of the environment while being independent of its content. We take first steps toward understanding and exploiting this PDE, and we examine its qualitative properties in relation to shape geometry. We analyze several cases in which the surface shape can be recovered in closed form, and we show that, under certain conditions, specular shape can be reconstructed when both the relative motion and the content of the environment are unknown. We discuss numerical issues related to the proposed reconstruction algorithms, and we validate our findings using both real and synthetic data.
KW - Gaussian curvature
KW - Specular objects
KW - environment motion field
KW - parabolic points
KW - shape reconstruction
KW - specular curvature
KW - specular flow
UR - http://www.scopus.com/inward/record.url?scp=78149280859&partnerID=8YFLogxK
U2 - 10.1109/TPAMI.2010.126
DO - 10.1109/TPAMI.2010.126
M3 - Article
C2 - 20847393
AN - SCOPUS:78149280859
SN - 0162-8828
VL - 32
SP - 2054
EP - 2070
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
IS - 11
M1 - 5499479
ER -