Adaptive linear lifting transform

1 . A method of mesh decoding, comprising:

receiving a bitstream that includes prediction information of a plurality of vertices in a mesh frame;

determining a prediction value of a current vertex of the plurality of vertices based on (i) a value of the current vertex received in the bitstream and (ii) a sum of ratios associated with a plurality of neighboring vertices of the current vertex, each of the ratios being equal to a value of a respective neighboring vertex of the plurality of neighboring vertices over a distance between the respective neighboring vertex and the current vertex; and

reconstructing the current vertex based on the prediction value of the current vertex.

2 . The method of claim 1 , wherein

the determining the prediction value of the current vertex further comprises:

determining an updated value of the current vertex, and

determining the prediction value of the current vertex as a sum of (i) the updated value of the current vertex and (ii) an average value of the plurality of neighboring vertices.

3 . The method of claim 2 , wherein the determining the updated value of the current vertex comprises:

determining the ratios associated with the plurality of neighboring vertices;

determining the sum of the ratios of the plurality of neighboring vertices;

determining a product of (i) a constant and (ii) the sum of the ratios of the plurality of neighboring vertices; and

determining the updated value of the current vertex as the value of the current vertex minus the product of (i) the constant and (ii) the sum of the ratios of the plurality of neighboring vertices.

4 . The method of claim 3 , wherein the constant is equal to a scalar constant over a total number of the plurality of neighboring vertices.

5 . The method of claim 1 , wherein the mesh frame is a selected mesh frame in a mesh sequence.

6 . The method of claim 1 , wherein the plurality of vertices is included in a selected region of the mesh frame.

7 . The method of claim 1 , wherein the plurality of vertices is included in a base layer of the mesh frame.

8 . The method of claim 1 , wherein the plurality of vertices is included in an enhancement layer of the mesh frame.

9 . The method of claim 1 , wherein the plurality of vertices is included in a selected frequency band of the mesh frame.

10 . A method of mesh encoding, comprising:

determining an initial prediction value of a current vertex of a plurality of vertices in a mesh frame based on (i) a value of the current vertex and (ii) each value of a plurality of neighboring vertices of the current vertex in the mesh frame;

determining an updated prediction value of the current vertex based on (i) the initial prediction value of the current vertex and (ii) a sum of ratios associated with the plurality of neighboring vertices of the current vertex, each of the ratios being equal to a value of a respective neighboring vertex of the plurality of neighboring vertices over a distance between the respective neighboring vertex and the current vertex; and

encoding the current vertex based on the updated prediction value of the current vertex into a bitstream.

11 . The method of claim 10 , wherein

the determining the initial prediction value of the current vertex further comprises:

determining the initial prediction value of the current vertex as (i) the value of the current vertex minus (ii) an average value of the plurality of neighboring vertices.

12 . The method of claim 11 , wherein the determining the updated prediction value of the current vertex comprises:

determining the ratios associated with the plurality of neighboring vertices;

determining the sum of the ratios of the plurality of neighboring vertices;

determining a product of (i) a constant and (ii) the sum of the ratios of the plurality of neighboring vertices; and

determining the updated prediction value of the current vertex as a sum of the initial prediction value of the current vertex and the product of (i) the constant and (ii) the sum of the ratios of the plurality of neighboring vertices.

13 . The method of claim 12 , wherein the constant is equal to a scalar constant over a total number of the plurality of neighboring vertices.

14 . The method of claim 10 , wherein the mesh frame is a selected mesh frame in a mesh sequence.

15 . The method of claim 10 , wherein the plurality of vertices is included in a selected region of the mesh frame.

16 . The method of claim 10 , wherein the plurality of vertices is included in a base layer of the mesh frame.

17 . The method of claim 10 , wherein the plurality of vertices is included in an enhancement layer of the mesh frame.

18 . The method of claim 10 , wherein the plurality of vertices is included in a selected frequency band of the mesh frame.

19 . A non-transitory computer-readable storage medium storing instructions which, when executed by a processor, cause the processor to perform a method of encoding a bitstream comprising:

determining an initial prediction value of a current vertex of a plurality of vertices in a mesh frame based on (i) a value of the current vertex and (ii) each value of a plurality of neighboring vertices of the current vertex in the mesh frame;

determining an updated prediction value of the current vertex based on (i) the initial prediction value of the current vertex and (ii) a sum of ratios associated with the plurality of neighboring vertices of the current vertex, each of the ratios being equal to a value of a respective neighboring vertex of the plurality of neighboring vertices over a distance between the respective neighboring vertex and the current vertex;

encoding the current vertex based on the updated prediction value of the current vertex into the bitstream; and

transmitting the encoded bitstream.

20 . The non-transitory computer-readable storage medium of claim 19 , wherein the determining the initial prediction value of the current vertex further comprises:

determining the initial prediction value of the current vertex as (i) the value of the current vertex minus (ii) an average value of the plurality of neighboring vertices.