This is a project for Calculus 2 students at Fitchburg State University. This project walks students through two examples of using definite integrals to determine the volume of objects: a bundt cake serves as the solid of revolution and the students build a structure from play dough that is not a solid of revolution.
Paper presented at ICCV 2019.
This paper targets the task with discrete and periodic
class labels (e.g., pose/orientation estimation) in the context of deep learning. The commonly used cross-entropy or
regression loss is not well matched to this problem as they
ignore the periodic nature of the labels and the class similarity, or assume labels are continuous value. We propose to
incorporate inter-class correlations in a Wasserstein training framework by pre-defining (i.e., using arc length of a
circle) or adaptively learning the ground metric. We extend
the ground metric as a linear, convex or concave increasing
function w.r.t. arc length from an optimization perspective.
We also propose to construct the conservative target labels
which model the inlier and outlier noises using a wrapped
unimodal-uniform mixture distribution. Unlike the one-hot
setting, the conservative label makes the computation of
Wasserstein distance more challenging. We systematically
conclude the practical closed-form solution of Wasserstein
distance for pose data with either one-hot or conservative
target label. We evaluate our method on head, body, vehicle and 3D object pose benchmarks with exhaustive ablation studies. The Wasserstein loss obtaining superior performance over the current methods, especially using convex mapping function for ground metric, conservative label,
and closed-form solution.
Xiaofeng Liu, Yang Zou, Tong Che, Peng Ding, Ping Jia, Jane You, B.V.K. Vijaya Kumar