Method and apparatus for representing image data using digital filtering and adaptive parameterization

A non-transitory computer-readable medium having executable instructions to cause a computer system to perform a method for encoding source data, the method comprising:

• defining a source polygon using parametric representation associated with the source data;
• identifying one or more portions of the source polygon, wherein each portion of the source polygon comprises a plurality of sample points;
• passing a filter throughout a sequence of samples representing the source polygon to obtain a filtered polygon;
• performing piecewise re-parameterization of each portion of the source polygon using a corresponding portion of the filtered polygon to obtain an updated sequence of samples representing the source polygon;
• and
• iteratively repeating the passing of the filter and the piecewise re-parameterization until a convergence condition is satisfied, to provide encoded data.

A system for encoding source data, comprising:

• a memory;
• and
• an encoder to define a source polygon based on a parametric representation associated with the source data, to identify one or more portions in the source polygon, wherein each portion in the source polygon comprises a plurality of sample points, to pass a filter throughout the source polygon, to perform piecewise re-parameterization of each segment of the source polygon to obtain an updated parametric representation of the source polygon, and to iteratively repeat the passing of the filter and the piecewise re-parameterization until a convergence condition is satisfied, to provide encoded data, wherein the encoder is to perform the piecewise re-parameterization of each portion of the source polygon by
• for each sample in a re-parameterized portion, computing a distance along the filtered polygon from a corresponding sample of the filtered polygon to an initial point, the initial point being a beginning of the filtered polygon or a beginning of the re-parameterized portion,
• storing, for each portion, resulting distances in a corresponding part of a re-parameterization table,
• normalizing, for each portion, the stored distances using a corresponding length-normalizing factor, and
• relocating samples along the source polygon in the portion being re-parameterized using normalized distances from a corresponding part of the re-parameterization table.

A system for encoding source data, comprising:

• a memory;
• an encoder to define a source polygon based on a parametric representation associated with the source data, to identify one or more portions in the source polygon, wherein each portion in the source polygon comprises a plurality of sample points, to pass a filter throughout the source polygon, to perform piecewise re-parameterization of each segment of the source polygon to obtain an updated parametric representation of the source polygon, and to iteratively repeat the passing of the filter and the piecewise re-parameterization until a convergence condition is satisfied, to provide encoded data;
• and
• a decoder to reconstruct the source data from the encoded data including
• forming an initial interpolation polygon using a sequence of samples within the encoded data as knots;
• up-sampling the interpolation polygon by inserting a set of extra samples in each interval between every two consecutive knots of the interpolation polygon, a number of extra samples being the same in each interval;
• passing a filter throughout a sequence of samples representing the up-sampled interpolation polygon;
• performing a piecewise update of each interval of the interpolation polygon using a corresponding portion of the filtered polygon as a reference interval;
• and
• repeating the passing of the filter and the piecewise update of each interval until a reconstruction condition is satisfied, wherein a last updated interpolation polygon represents reconstructed source data.