IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995
We show how to automatically acquire Euclidian shape representations of objects from noisy image ... more We show how to automatically acquire Euclidian shape representations of objects from noisy image sequences under weak perspective. The proposed method is linear and incremental, requiring no more than pseudoinverse. A nonlinear, but numerically sound preprocessing stage is added to improve the accuracy of the results even further. Experiments show that attention to noise and computational techniques improves the shape results substantially with respect to previous methods proposed for ideal images
... By equating the first and last term, we obtain the following equation relating the image grad... more ... By equating the first and last term, we obtain the following equation relating the image gradient g, the inter-frame displacement d, and the difference h between image intensities: ... The total image displacement from first to last frame is about 100 pixels (one pixel per frame). 10 ...
Inferring scene geometry and camera motion from a stream of images is possible in principle, but ... more Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion without computing depth as an intermediate step.An image stream can be represented by the
Inferring scene geometry and camera motion from a stream of images is possible in principle, but ... more Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step. An image stream can be represented by the 2F×P measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filled-in measurement matrix that may result from occlusions or tracking failures. The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.
... Carlo Tomasi and Takeo Kanade School of Computer Science Carnegie Mellon University Pittsburg... more ... Carlo Tomasi and Takeo Kanade School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 ... The rank theorem captures precisely the nature of the redundancy of an image sequence, and allows deal-ing with a large number of points and frames in a con ...
Inferring scene geometry and camera motion from a stream of images is possible in principle, but ... more Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step. An image stream can be represented by the 2F×P measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filled-in measurement matrix that may result from occlusions or tracking failures. The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.
Inferring the depth and shape of remote objects and the camera motion from a sequence of images i... more Inferring the depth and shape of remote objects and the camera motion from a sequence of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. This problem is overcome by inferring shape and motion without computing depth as an intermediate step. On a single epipolar plane, an image sequence
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995
We show how to automatically acquire Euclidian shape representations of objects from noisy image ... more We show how to automatically acquire Euclidian shape representations of objects from noisy image sequences under weak perspective. The proposed method is linear and incremental, requiring no more than pseudoinverse. A nonlinear, but numerically sound preprocessing stage is added to improve the accuracy of the results even further. Experiments show that attention to noise and computational techniques improves the shape results substantially with respect to previous methods proposed for ideal images
... By equating the first and last term, we obtain the following equation relating the image grad... more ... By equating the first and last term, we obtain the following equation relating the image gradient g, the inter-frame displacement d, and the difference h between image intensities: ... The total image displacement from first to last frame is about 100 pixels (one pixel per frame). 10 ...
Inferring scene geometry and camera motion from a stream of images is possible in principle, but ... more Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion without computing depth as an intermediate step.An image stream can be represented by the
Inferring scene geometry and camera motion from a stream of images is possible in principle, but ... more Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step. An image stream can be represented by the 2F×P measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filled-in measurement matrix that may result from occlusions or tracking failures. The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.
... Carlo Tomasi and Takeo Kanade School of Computer Science Carnegie Mellon University Pittsburg... more ... Carlo Tomasi and Takeo Kanade School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 ... The rank theorem captures precisely the nature of the redundancy of an image sequence, and allows deal-ing with a large number of points and frames in a con ...
Inferring scene geometry and camera motion from a stream of images is possible in principle, but ... more Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step. An image stream can be represented by the 2F×P measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filled-in measurement matrix that may result from occlusions or tracking failures. The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.
Inferring the depth and shape of remote objects and the camera motion from a sequence of images i... more Inferring the depth and shape of remote objects and the camera motion from a sequence of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. This problem is overcome by inferring shape and motion without computing depth as an intermediate step. On a single epipolar plane, an image sequence
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