Published on February 25, 2014
What’s so good about pieces, Lego and understanding? Anton van den Hengel Australian Centre for Visual Technologies (ACVT) The University of Adelaide South Australia
People think in 3D
It has been a theme … "the perception of solid objects is a process which can be based on the properties of three-dimensional transformations and the laws of nature” Larry Roberts (1965)
Geometry is not enough
Structure and semantics interact
Structure and geometry interact
WHY PLANTS ARE LIKE LEGO
Developmental changes in response to drought The escape response of Clipper under drought is reflected in an earlier time of absolute maximum growth 46 d after sowing Absolute growth rate [mm2 d-1] 7000 6000 5000 well watered 4000 39 d after sowing 3000 2000 drought 1000 0 30 35 40 45 50 Time after sowing [d] 55 60 65 Boris Parent, ACPFG
Morphological changes in response to drought Relative ratio of shoot area / height The reduced number of tillers under drought is reflected in the area/height ratio 3 2.8 2.6 well watered 2.4 2.2 2 1.8 1.6 1.4 drought 1.2 Barley cv Clipper 1 30 40 50 Time after sowing [d] 60 Boris Parent, ACPFG
Deep reasoning • • • Try to explain as much as possible Fine-grained and detailed Deep semantics • • And the implied constraints Shape is only an intermediate step
Silhouettes • We’re only interested in shape (at least for now)
Deconstruction • • • Render all possible building blocks in every possible position, and recover its silhouette Then reconstruct object silhouettes from templates Requires enough camera information to achieve this
Template shapes • nTemplates = nShapes x nPositions x nRotations • So there are lots of them But they are sparsely used •
Sparse recovery • • • • alpha a vector of binary template coefficients Pi a matrix with one template silhouette per column y the silhouette of the shape to be recovered NP hard and fragile
Sparse recovery – L_1 norm • But there may still be millions of templates, and they’re enormous (|Pixels| x |Images|)
Sparse recovery – Random projections • Random projection by DxS matrix Phi D << S • Phi is sparsely sampled from N(0,1) • • But there are still too many templates
Sparse recovery - Cropping • • Eliminate templates with a footprint that extends significantly beyond that of the object Reduces the number of templates by at least an order of magnitude • Down to tens to tens of thousands of templates
Binarising the solution • • Solutions are not binary Randomly generate binary hypotheses from nonbinary alpha • Evaluate using an accurate composition model
Fraction of True Leaves Recovered Results Max Search Viable 0.9 0.8 0.7 0.6 200 400 600 Number of Templates 800 1000
Fraction of Pixels Explained Results 0.08 0.06 0.04 Max Search 0.02 0 0 0.01 0.02 0.03 0.04 Noise Level (Fraction of Pixels Changed) 0.05 0.06
Composition problems Not a true model of silhouette formation So doesn’t deal well with template overlap Working on this by subtracting overlaps, graph-based approaches Somewhat overcome by…
Inequality • Isn’t physically accurate for foreground pixels, so split • Background (0) pixels • And foreground pixels
Practicality again • Only interested in the number of pixels outside the object silhouette, not the location So not • but •
Practicality again • Want to ensure that • Need to project to a lower dimension • But Phi_I must have only positive elements
A better model of composition • Left with
Constraints - Intersection
Constraints - Intersection • Form J where every row represents a constraint • If templates i and k intersect then insert a row in J with only elements i and k set to 1
Constraints - Support • Form K where every row represents a constraint If template i needs support t set K_ii = t • If template j provides s support to j then K_ij = -s •
Measurement benefit tails off Accuracy vs noise for varying numbers of measurements Accuracy (fraction of true blocks recovered) 1 49 441 1225 2401 3969 5929 8281 11025 0.9 0.8 0.7 0.6 0.5 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 Noise level (added to camera extrinsics) 0.35 0.4
Limitations • One template per value per parameter • Fixable?
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