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.
◆ arm_bilinear_interp_f32()
Floating-point bilinear interpolation.
- Parameters
-
[in,out] | *S | points to an instance of the interpolation structure. |
[in] | X | interpolation coordinate. |
[in] | Y | interpolation coordinate. |
- Returns
- out interpolated value.
Definition at line 7137 of file arm_math.h.
◆ arm_bilinear_interp_q15()
Q15 bilinear interpolation.
- Parameters
-
[in,out] | *S | points to an instance of the interpolation structure. |
[in] | X | interpolation coordinate in 12.20 format. |
[in] | Y | interpolation coordinate in 12.20 format. |
- Returns
- out interpolated value.
Definition at line 7281 of file arm_math.h.
◆ arm_bilinear_interp_q31()
Q31 bilinear interpolation.
- Parameters
-
[in,out] | *S | points to an instance of the interpolation structure. |
[in] | X | interpolation coordinate in 12.20 format. |
[in] | Y | interpolation coordinate in 12.20 format. |
- Returns
- out interpolated value.
Definition at line 7205 of file arm_math.h.
◆ arm_bilinear_interp_q7()
Q7 bilinear interpolation.
- Parameters
-
[in,out] | *S | points to an instance of the interpolation structure. |
[in] | X | interpolation coordinate in 12.20 format. |
[in] | Y | interpolation coordinate in 12.20 format. |
- Returns
- out interpolated value.
Definition at line 7361 of file arm_math.h.