Detection of the intersection lines in multiplanar environments: Application to real-time estimation of the camera-scene geometry
Summary (2 min read)
Results
- Dynein mediates eR association with centrosomal Mts during late interphase.
- VP16-driven Dhc64C RNAi spermatocytes the ER was entirely excluded from centrosomal MTs, resulting in complete absence of the peri-centrosomal concentration of ER seen in controls (Fig. 1a), also known as Strikingly, in bam-GAL4.
- Together, these results indicated that dynein mediates the association of the ER with MTs, and functions to focus the ER around MT minus-ends at centrosomes in late interphase Drosophila spermatocytes.
- Accordingly, the authors next sought to determine whether this astral MT association of ER and concentration around spindle pole centrosomes in M-phase depends on dynein activity, similar to what they observed in late interphase.
- As shown in Figs 2a, 3a, Supplementary Videos 1 and 2, the first visible event of Control a.
Dhc64C
- RNAi Merge Merge 5 µm 5 µm 5 µm 5 µm Figure 1. Dynein is required for ER concentration around centrosomes in late interphase.
- (a) Representative images of control (upper panel) and Dhc64C RNAi (lower panel) spermatocytes co-expressing GFP-tubulin and RFP-KDEL (red) during late interphase.
- This dramatic redistribution of the ER from the cytoplasm to astral MTs around the centrosomes was clearly reflected by a four-fold increase in ERcentrosome/ ERcytoplasm at metaphase as compared to late interphase (6.45 ± 0.26 at metaphase vs. 1.60 ± 0.06 at interphase; Fig. 1c,d).
- Filled arrowheads indicate visible centrosomes, and open arrowheads indicate the approximate location of centrosomes that are out of the focal plane.
Discussion
- Proper distribution of the ER in dividing cells is critical, because it ensures that progeny cells receive necessary proportions of this essential organelle.
- Dynein independent ER redistribution to centrosomes requires MTs. Control (a) and Dhc64C (b) RNAi spermatocytes expressing GFP-tubulin and RFP-KDEL (red) were imaged beginning in late interphase before the commencement of ER redistribution to the centrosomes.
- In conclusion, the authors have demonstrated that an M-phase specific mechanism associates the ER with astral MTs and partitions the organelle to spindle poles in dividing cells.
- Surprisingly, and in contrast to many previous suggestions, this ER localization is not mediated by dynein or other known MT minus-end motors.
Materials and Methods
- Lines carrying RNAi targeting Klp61F and ncd were obtained from the Vienna Drosophila Resource Center (Stock# 109280 and 110255, respectively).
- Controls for RNAi experiments were therefore carried out by crossing RNAi animals to w1118.
- For colchicine treatments, whole testes were placed in a glass-bottom dish filled with Schneider’s medium.
- The average RFP-KDEL fluorescence intensity within a 2.5 µm diameter circle immediately adjacent to the centrosome was then obtained using ImageJ.
- Ratios were calculated at 2 min intervals, and the Z-plane of the images used was adjusted over time as needed to follow the same centrosome.
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Citations
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4 citations
Cites background from "Detection of the intersection lines..."
...This paper is an expanded version of [25]....
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Cites background or methods from "Detection of the intersection lines..."
...Most of the AR markerless approaches [12,21,22] are based on feature point tracking and commonly fail with untextured planes unless some flaws are present on the surface....
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...In [21], the authors used a similar consistency approach to [2] and realized that detecting the projection of the intersection line between any two planes gives enough information to build a polyhedral representation of the environment, although these projections are just intermediate results toward the Euclidean reconstruction of planes....
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...The use of planar surfaces for camera localization and structure recovery has recently received attention from the computer vision [2,21,22] and robotics [8,23] communities, because the presence of planar surfaces in man-made environments is common: planes are present as walls, doors, posters, books, facades, desks and other furniture....
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Cites background or methods from "Detection of the intersection lines..."
...The use of our framework for video processing is direct and may require non-linear filtering theory as has been shown in [2,7]....
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...The use of planar surfaces for camera localization and structure recovery have recently received attention from the computer vision community [2,7,8,10,11]....
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...In [7] he shows how to recover the localization and reconstruction parameters of multi-planar scenes with minimal user assistance, which consists of manual selection of a base plane, additional planes are considered as...
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...The intersection between planes [7] i and j implies that a given point x belonging to this intersection satisfies x ′ ∼ Hix and x ∼ Hjx....
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1 citations
Cites background or methods from "Detection of the intersection lines..."
...Although there exist some works intending to deal with these problems, most of them are based on the estimation of the epipolar geometry, non-linear optimization, or linear systems that do not incorporate geometrical consistency and may produce undesirable side-effects....
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...…induced by planarity in the scene in order to estimate calibration, localization and reconstruction by using only linear systems of equations, instead of solving non-linear problems with the corresponding instability due to errors in the initial parameters guess or multi-linear problems....
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References
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...The core of this system is a robust and accurate procedure for detecting the intersection line between two planes....
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...The core of this system is a robust and accurate procedure for detecting the intersection line between two planes....
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Frequently Asked Questions (14)
Q2. What are the future works mentioned in the paper "Detection of the intersection lines in multiplanar environments: application to real-time estimation of the camera-scene geometry" ?
The authors presented a method for tracking and mapping in multiplanar environments, which has been validated on both synthetic and real-size ( spatially and temporally ) experiments. This method may be extended to allow detection and reconstruction of other kinds of features like the edges of the scene.
Q3. What is the main characteristic of the Levenberg-Marquardt algorithm?
An intuitive interface controlled by only four keys is used to define blobs, indicate the PF convergence, and validate or invalidate the initial and further Euclidean reconstructions.
Q4. What is the core of their system?
The core of their system is an accurate and robust procedure for detecting the projection of the intersection line between two planes based on their apparent motion.
Q5. What is the significance of the pruning?
A significant pruning is obtained by computing a single global HT updated from frame to frame by transferring the line candidates of image i to image 1, using the homography Hik −T , k = 1 or k = 2: doing that, only the projections of the lines on plane πk contribute to the local maxima of the HT (other lines are transferred to unstable coordinates of the HT).
Q6. What is the key idea of particle filtering?
The key idea is to represent the required posterior density function p(xi|z1:i), where z1:i is the set of all available measurements up to time i, by a set of random samples with associated weights wji , and to compute estimates based on these samples and weights:p(xi|z1:i) ≈N ∑j=1wji δ(xi − x j i ),N ∑j=1wji = 1.
Q7. What is the simplest way to compute the 2 of the cameraplane?
any value of λ induces a homography H(λ) = d2(λ)R+tn2(λ)T [4], providing transfer errors ||z (H(λ)vi) − z (H2vi) ||.When no information is available about the cameraplanes geometry, structure and motion are computed using a higher degree optimization that requires an initial estimate.
Q8. What is the eigenvector associated to the simple eigenvalue of T?
The 3 × 3 matrix T = HT 1 H−T 2 is a homology, which admits a pencil of globally fixed lines intersecting at the epipole e and a distinct fixed line corresponding to the projection l of the intersection line between π1 and π2.l is therefore the eigenvector associated to the simple eigenvalue of T.
Q9. What is the simplest way to compute the svd?
A Gaussian noise of standard deviation 0.3 was added to the coordinates of the points used to compute the inter-image homographies.
Q10. What is the simplest way to obtain a homography?
Synthetic tests have been performed in order to assess the effects of the number of particles N and the resampling threshold Nt over the convergence of the PF.
Q11. How many iterations of the Levenberg-Marquardt algorithm?
the mean number of iterations of the Levenberg-Marquardt algorithm is 3.9 for the 9-parameters optimization, against 6.7 for the 11-parameters optimization.
Q12. What is the method used to create a new blob?
When a new horizontal blob is defined, it is back-projected using the known equation of the horizontal plane in the camera coordinate system.
Q13. What is the type of scene that is considered?
A “ground and wall” type of scene is considered: two circles are displayed, one on the bottom half and the other on the top half of the screen, that allow the user to “capture” blobs on the ground plane and (resp.) the vertical planes (see Fig. 5, top frame).
Q14. What is the probability density of the line?
the particles are uniformly distributed inside the largest ellipse E contained in the image (Fig.2, first frame);(ii) the prior p(xi|xi−1) is the normal distribution centered at xi−1 with covariance matrix V (V = diag2([0.01, 0.01, 5]) in their experiments); the importance density is the prior;(iii) the likelihood density at time i is given by:p(zi|xi) = p(z g i |xi)p(z p i |xi),where zgi and z p i are (assumed independent) geometric and (resp.) photometric measurements the authors now detail.