  In this work, we present a solution to the challenging problem of
reconstructing liquids from image data. The challenges in reconstructing
liquids, which is not faced in previous reconstruction works on rigid and
deforming surfaces, lies in the inability to use depth sensing and color
features due the variable index of refraction, opacity, and environmental
reflections. Therefore, we limit ourselves to only surface detections (i.e.
binary mask) of liquids as observations and do not assume any prior knowledge
on the liquids properties. A novel optimization problem is posed which
reconstructs the liquid as particles by minimizing the error between a rendered
surface from the particles and the surface detections while satisfying liquid
constraints. Our solvers to this optimization problem are presented and no
training data is required to apply them. We also propose a dynamic prediction
to seed the reconstruction optimization from the previous time-step. We test
our proposed methods in simulation and on two new liquid datasets which we open
source so the broader research community can continue developing in this under
explored area.
