Bilinear Interpolation
[Interpolation Functions]

Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid. More...

Detailed Description

Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.

The underlying function f(x, y) is sampled on a regular grid and the interpolation process determines values between the grid points. Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension. Bilinear interpolation is often used in image processing to rescale images. The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types.

Algorithm

The instance structure used by the bilinear interpolation functions describes a two dimensional data table. For floating-point, the instance structure is defined as:

   typedef struct
   {
     uint16_t numRows;
     uint16_t numCols;
     float32_t *pData;
 } arm_bilinear_interp_instance_f32;
 

where numRows specifies the number of rows in the table; numCols specifies the number of columns in the table; and pData points to an array of size numRows*numCols values. The data table pTable is organized in row order and the supplied data values fall on integer indexes. That is, table element (x,y) is located at pTable[x + y*numCols] where x and y are integers.

Let (x, y) specify the desired interpolation point. Then define:

     XF = floor(x)
     YF = floor(y)
 

The interpolated output point is computed as:

  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
           + f(XF+1, YF+1) * (x-XF)*(y-YF)
 

Note that the coordinates (x, y) contain integer and fractional components. The integer components specify which portion of the table to use while the fractional components control the interpolation processor.

if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output.

Function Documentation