The split of training, validation and test sets follows the settings of the previous method[10]. The inputpointcloudconsists of2048pointsrepresented bytheirEuclidean coordinates sampled from a normalized object, and the indexes of keypoints are given. The learning rate is set to1 10 3 andhalvedevery10epochs. Wesetthetargetvarianceσ2t to4,thelossweight ofvariance regularization to1, and the loss weight of distributions regularization to0.01 to achieve the best results after tuning. Wesetthetargetvarianceσ2t to4,thelossweightofvariance regularization to1, and the loss weight of distributions regularization to0.01 to achieve the best results after tuning.

In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models.

In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models.

Next consider the case where[ti,ti+1] lies in a range[t`,tr] over which the camera ray is exiting the surface, i.e. the signed distance function is increasing onp(t) over [t`,tr]. Then we have ( f(p(t)) v) < 0 in [ti,ti+1]. Then, according to Eqn. 1, we haveρ(t) = 0. Therefore, by Eqn.12ofthepaper,wehave αi=1 exp Recall that our S-density fieldφs(f(x)) is defined using the logistic density functionφs(x) = se sx/(1+e sx)2, which is the derivative of the Sigmoid functionΦs(x) = (1+e sx) 1, i.e. φs(x)=Φ0s(x). As a first-order approximation of signed distance functionf, suppose that locally the surface is tangentially approximated byasufficiently small planar patch with itsoutwardunitnormal vector denotedas n. Nowsupposep(t)isapoint on the surfaceS,that is, f(p(t)) = 0. Next we will examine the value ofdwdt(t) at t = t . Thesigneddistancefunction f ismodeledbyanMLP that consists of 8hidden layers with hidden size of 256.

Neural Information Processing Systems http://nips.cc/

Let S = {( 1,y1),...,( n,yn)}.

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