Geometric modelization of images and applications

The method according to 45 and wherein said morphing texture comprises:

• enabling interactive prescription of a morphing operation;
• applying a standard mathematical extension F of said prescribed morphing to an entire said image;
• applying said F to each geometric parameter of said texture in turn, wherein said parameters comprise at least said chains of elements, said singularities, and widths of said color profiles;
• preserving brightness parameters of said color profiles;
• and
• returning said texture models to their original background domains.

An image compression method implemented on a computing device, the method comprising:

• geometrically modelizing an image;
• filtering each model created in said modelizing with quality control as per an allowed reconstruction error A_0;
• for each singular point, saving type of normal form (NF) in list LNF together with parameters of normalizing transformation NT;
• saving chains of graphs G_j according to combinatorial type, vertices coordinates and parameters of spline curves representing each EME's chains, joining said vertices;
• approximating parameters of color profiles of said EMEs along said chains with a prescribed accuracy A_1;
• quantizing geometric parameters of said models up to accuracy A_2;
• aggregating each of said parameters of said models according to their expected correlations;
• and
• organizing said aggregated parameters according to type in files.