Hölder adaptive image synthesis

A device rendering at least partially an image of a three-dimensional scene on an image plane (I), said device including computer storage, and a processor connected to said computer storage, said processor being programmed to:

• construct a luminosity function in at least a region of the image plane as equivalent to a first linear combination, wherein the first linear combination comprises terms and involves functions of at least a subset of a first set of functions defined on the image plane;
• determining values of coefficients of the first linear combination by solving a first linear system, wherein the first linear system is obtained by imposing a value of a second linear combination at each point of at least a sub-subset of a first subset of the image plane to be equal to sampled values of luminosity at said point, wherein the second linear combination involves at least the terms of the first linear combination;
• store values of those coefficients of the second linear combination which are also comprised in the first linear combination and at least an information needed to associate each coefficient of the first linear combination to a corresponding function of the first set of functions, wherein the corresponding function of the first set of functions multiplies said each coefficient in the first linear combination;
• and encode at least a luminosity of the image with the luminosity function;
• wherein the first set of functions is at least a subset of a basis and/or frame of an inner product space and comprises each function that belongs to a second set of functions and satisfies a selection condition associated to said function, wherein the selection condition associated to said function depends at least on said function and on a set of stored input data, wherein the set of stored input data describes, at least in part, the three dimensional scene;
• wherein the first subset of the image plane comprises points and wherein the points of the first subset of the image plane are distributed according to a first distribution criterion, wherein the first distribution criterion depends on at least a location of support of at least some elements of the first set of functions on the image plane.

One or more non-transitory computer-readable media comprising instructions that cause a computer device, in response to execution of the instructions by a processor of the computer device, to:

• construct a luminosity function in at least a region of the image plane as equivalent to a first linear combination, wherein the first linear combination comprises terms and involves functions of at least a subset of a first set of functions defined on the image plane;
• determining values of coefficients of the first linear combination by solving a first linear system, wherein the first linear system is obtained by imposing a value of a second linear combination at each point of at least a sub-subset of a first subset of the image plane to be equal to sampled values of luminosity at said point, wherein the second linear combination involves at least the terms of the first linear combination;
• store values of those coefficients of the second linear combination which are also comprised in the first linear combination and at least an information needed to associate each coefficient of the first linear combination to a corresponding function of the first set of functions, wherein the corresponding function of the first set of functions multiplies said each coefficient in the first linear combination;
• and encode at least a luminosity of the image with the luminosity function;
• wherein the first set of functions is at least a subset of a basis and/or frame of an inner product space and comprises each function that belongs to a second set of functions and satisfies a selection condition associated to said function, wherein the selection condition associated to said function depends at least on said function and on a set of stored input data, wherein the set of stored input data describes, at least in part, the three dimensional scene;
• wherein the first subset of the image plane comprises points and wherein the points of the first subset of the image plane are distributed according to a first distribution criterion, wherein the first distribution criterion depends on at least a location of support of at least some elements of the first set of functions on the image plane.