Removing Photography Artifacts Using Gradient Projection and Flash-Exposure Sampling

Photographing through glass can capture reflections of objects in front of it. In this example, the ambient photograph reveals the photographer’s face, hands, and tripod. The short-exposure flash photograph suppresses those reflections but adds a hotspot from the glossy painting surface.

In a patch without reflections, the flash and ambient image gradients point in the same direction. Where reflections overlap the scene, the ambient gradient direction is perturbed. The method uses gradient direction as a quasi-invariant under illumination changes.

Constrain the ambient-image gradient direction by projecting each ambient gradient vector onto the corresponding flash-image gradient vector. A 2D integration of the projected field produces the result image.

The gradients removed by projection form a residual field. Integrating that residual gives the reflection layer, decomposing the original image into a reflection-reduced image and the removed reflections.

Knowing a gradient’s desired direction still leaves its magnitude unspecified. Projection selects a component in that direction while removing the orthogonal component.

For an integrable gradient field, rotating every gradient vector by 90° produces a divergence-free field. Reconstruction from that field has no image structure, up to the choice of boundary conditions and additive constant.

The illustrated experiment rotates gradients computed from the Lena image and reconstructs an image at each angle. At 90°, visual information disappears; at 180°, the reconstruction is the negative of the original image.