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Existing models, however, are based on a Euclidean representation of shape deformations. In contrast, we argue that shape has a manifold structure: For example, averaging the shape deformations for two people does not necessarily yield a deformation corresponding to a valid human shape, nor does the Euclidean difference of these two deformations provide a meaningful measure of shape dissimilarity. Consequently, we define a novel manifold for shape representation, with emphasis on body shapes, using a new Lie group of deformations.
This has several advantages. First , we define triangle deformations exactly, removing non-physical deformations and redundant degrees of freedom common to previous methods. Third , the group structure allows the valid composition of deformations. This is important for models that factor body shape deformations into multiple causes or represent shape as a linear combination of basis shapes.
Similarly, interpolation between two mesh deformations results in a meaningful third deformation. Instead of modeling Euclidean shape variation with Principal Component Analysis we capture shape variation on the manifold using Principal Geodesic Analysis. Our experiments show consistent visual and quantitative advantages of Lie Bodies over traditional Euclidean models of shape deformation and our representation can be easily incorporated into existing methods.
This project is part of a larger effort that brings together statistics and geometry to model statistics on manifolds. Freifeld, O. Abstract Three-dimensional object shape is commonly represented in terms of deformations of a triangular mesh from an exemplar shape. In contrast, we argue that shape has a manifold structure: For example, summing the shape deformations for two people does not necessarily yield a deformation corresponding to a valid human shape, nor does the Euclidean difference of these two deformations provide a meaningful measure of shape dissimilarity.
First we define triangle deformations exactly, removing non-physical deformations and redundant degrees of freedom common to previous methods. Second, the Riemannian structure of Lie Bodies enables a more meaningful definition of body shape similarity by measuring distance between bodies on the manifold of body shape deformations. Third, the group structure allows the valid composition of deformations.
Finally, body shape variation is modeled using statistics on manifolds.
This is how our bodies betray us in a lie
The migrant caravan is a group of people making a concerted effort together to try to reach and enter the US. The 2,mile-long US-Mexico border has sometimes been a deadly crossing between ports of entry. A total of migrant deaths were recorded last year. The death toll so far this year has not been released. Elsewhere, three children and an adult from Honduras died in April after their raft capsized on the Rio Grande.
Between Bodies Lie by H.M. Blanc
He has not given a reason for his departure. Democrats in the House of Representatives have already approved the humanitarian aid but the bill faces a tough route through the upper chamber, the Republican-controlled Senate.
President Donald Trump said he did not seek Mr Sanders' resignation and added he did not think he had ever met him. Mr Trump's hardline stance on immigration has come under intense scrutiny recently, as conditions inside border patrol facilities were found to be poor, with inadequate food and a lack of medical care.
At a migrant centre in Clint, Texas, lawyers found that several children had flu and a two-year-old without a nappy was being watched over by two older children.
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They also saw children in soiled clothing, covered in urine and faeces, with many of them not having washed since they entered the facility weeks ago. Lawyers also reported children were "locked up in horrific cells where there's an open toilet in the middle of the room". After the findings, an official said that nearly children had been moved from the facility, but staff have since moved a third of those back into Clint. Mr Trump has said he is "very concerned" over the conditions at the border, but claims things are better than they were under the previous administration.
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Rebuking Mr Trump, Michael Bochenek, a lawyer for Human Rights Watch, said: "We did not have the kind of overcrowded conditions for unaccompanied kids in Border Patrol holding cells like we saw in Clint. Watch Live.
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Outrage as dad and daughter's bodies lie face down in river - Warning: Distressing images. By Adam Arnold, news reporter. Fill 2 Copy 11 Created with Sketch. Friday 28 June , UK. Why you can trust Sky News.