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ICCV 2007 tutorial Gradient-domain methods

Gradient Domain Manipulation Techniques in Vision and Graphics

Amit Agrawal and Ramesh Raskar

Mitsubishi Electric Research Laboratories

The idea

Manipulate gradients. Reconstruct images and surfaces.

Gradient-domain techniques work with changes in image intensity or surface shape rather than directly editing pixel values or geometry. This course connects the mathematical foundations of gradient fields with applications in computer vision and graphics, from high dynamic range tone mapping and seamless image editing to video synthesis and 3D surface reconstruction.

Gradient-domain pipeline: compute image gradients, modify the gradient field, and integrate it to reconstruct the output image or video.
A common pipeline: estimate gradients, transform them, and integrate the modified field to synthesize the result.
Overview connecting gradient estimation and manipulation with reconstruction of images, videos, meshes, and surfaces.
Both measured and manipulated gradients can produce non-integrable fields. Reconstruction methods turn these fields into images or surfaces.

Course topics

From vector fields to practical tools

The course covers curl, divergence, and integrability; when it is useful to operate on gradients; and the numerical methods needed to reconstruct images and surfaces.

Foundations
Vector fields, integrability, Poisson reconstruction, and boundary conditions.
Image manipulation
Tone mapping, image matting, seamless cloning, reflection removal, and image fusion.
Video & geometry
Video editing, surface reconstruction, and gradient-based mesh editing.
Implementation
Numerical methods, gradient-integration pseudocode, and downloadable C++ and MATLAB tools.
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Course materials