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.
