Media item relighting technique

A non-transitory, computer-readable, programmable product, for use in conjunction with a computing device, comprising code, executable by the computing device, for causing the computing device to do the following:

• illuminate at least a portion of the media item by a light source of the computing device;
• send a synchronization signal to another computing device to instruct the other computing device to record a video of the at least a portion of the media item;
• track a random and varying velocity trajectory of the computing device;
• receive media item frames of the media item recorded by the other computing device;
• determine a position of the light source for at least some of the media item frames for obtaining a light transport function;
• determine, without using 3D geometry of the media item in the determination, in a first signal domain, the light transport function describing the appearance of a particular media element under different illumination conditions, as produced with a light source, at least partly defined by positions of the light source used to illuminate the particular media element;
• sample, in the first signal domain, the light transport function of the particular media element to obtain discrete data samples of the light transport function;
• project the data samples, in the first signal domain, into a sampling grid to obtain a spatially sparsely and non-uniformly sampled light transport function;
• convert the spatially sparsely and non-uniformly sampled light transport function into a transform signal domain referred to as a second signal domain by using a mathematical operation;
• interpolate, in the second signal domain, using compressive sensing, the sparsely and non-uniformly sampled light transport function to obtain a light transport matrix in the second signal domain;
• and
• transform the light transport matrix into the first signal domain to obtain a substantially uniformly sampled light transport matrix to produce a relighted media element suitable to be displayed on a display.

A method of relighting a media item comprising media elements, the method comprising, for at least some of the media elements:

• a first mobile computing device illuminating at least a portion of the media item by a light source of the first mobile computing device;
• the first mobile computing device moving along a random trajectory at a varying velocity to thereby illuminate the at least a portion of the media item by the light source;
• the first mobile computing device tracking the trajectory;
• the first mobile computing device receiving media item frames of the media item recorded by a second computing device;
• the first mobile computing device determining a position of the light source for at least some of the media item frames for obtaining a light transport function;
• the first mobile computing device determining, without using 3D geometry of the media item in the determination, the light transport function, in a first signal domain, describing the appearance of a particular media element under different illumination conditions at least partly defined by positions of the light source used to illuminate the particular media element;
• the first mobile computing device sampling in the first signal domain the light transport function of the particular media element to obtain discrete data samples of the light transport function;
• the first mobile computing device projecting the data samples, in the first signal domain, into a sampling grid to obtain a spatially sparsely and non-uniformly sampled light transport function;
• the first mobile computing device interpolating in a transform signal domain referred to as a second signal domain, by performing compressive sensing of the sparsely and non-uniformly sampled light transport function to obtain a light transport matrix in the second signal domain;
• and
• the first mobile computing device transforming the light transport matrix from the second signal domain into the first signal domain to obtain a substantially uniformly sampled light transport matrix to produce a relighted media item suitable to be displayed on a display.