Shape from Heat Conduction

Shape Recovery for Visibly Transparent or Translucent objects

Our results below focus on objects with diverse visible reflectance properties, including those that are transparent or translucent to visible light. The visualized iso-contour temperature lines in the second column indicate observable heat flow in the thermal spectrum. Interestingly, these patterns are observable even for objects that appear visually transparent or translucent enabling reconstructions of such objects, which are otherwise challenging using conventional vision techniques.

(Reconstructions shown on the right are interactive.)

More Qualtitative Results

We show results on a variety of objects with different shapes and materials, including plastic bottles, a 3D-printed bunny, an aluminum soda can, and acrylic items like a ball, bear, and pineapple. Imaged with a thermal camera under uncalibrated lighting, the captured heat flow visualizes iso-contour lines of temperature which are used to estimate the object's shape.

(Hover over the heat-flow videos to reveal the imaged object)

Heating Objects using a Hot Air Blower

To demonstrate that heat transport can be induced more broadly than just using light bulbs, we ask the question: can we heat up objects in other ways and still reconstruct their shape? We can indeed! Here, we show results from heating objects using a hot air blower. The heat flow captured in the thermal videos is used to estimate the object's shape.

Reconstructions from Natural Cooling

Do you always need to heat objects to reconstruct their shape? Not necessarily! Here, we show results from objects cooling down naturally after being heated. The heat flow captured in the thermal videos is used to estimate the object's shape.

Image Formation in Thermal

In the visible spectrum, an object's appearance is determined solely by light transport effects, which can be characterized through BSDF of the material. However, accurately modeling thermal appearance requires considering not only light transport effects like reflections but also heat transport within and around the object.

Modeling Heat Transport

Heat transport within an object and its surroundings is described by the transient heat equation, which incorporates all three modes of heat transfer: conduction, convection, and radiation. Here, conduction within an object is modeled through a shape-dependent Laplacian term. Retrieving this Laplacian from thermal videos is the key to our approach.

Solution to the Linearized Heat Equation

The resulting linearized discrete heat equation is non-linear to shape but linear with respect to the unknowns of the Laplace Operator. Solving the linearized form across timeframes of a thermal video, yields scene, material, and geometric properties such as scaled heat capacity, convection coefficient, absorbed heat flux, and the shape-dependent Laplace Operator.

Shape from Laplacian

Estimating shape from Laplacian is challenging due to its non-convex nature and multiple global minima. We draw insights from the absorbed heat flux images using two uncalibrated light sources to resolve the inherent shape ambiguities. Our physics-based optimization objective adjusts mesh vertices along the camera rays to retrieve the shape of the object.

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