Bilinear Interpolation

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. More...

Collaboration diagram for Bilinear Interpolation:

Functions
__STATIC_FORCEINLINE float32_t	arm_bilinear_interp_f32 (const arm_bilinear_interp_instance_f32 *S, float32_t X, float32_t Y)
	Floating-point bilinear interpolation. More...
__STATIC_FORCEINLINE q15_t	arm_bilinear_interp_q15 (arm_bilinear_interp_instance_q15 *S, q31_t X, q31_t Y)
	Q15 bilinear interpolation. More...
__STATIC_FORCEINLINE q31_t	arm_bilinear_interp_q31 (arm_bilinear_interp_instance_q31 *S, q31_t X, q31_t Y)
	Q31 bilinear interpolation. More...
__STATIC_FORCEINLINE q7_t	arm_bilinear_interp_q7 (arm_bilinear_interp_instance_q7 *S, q31_t X, q31_t Y)
	Q7 bilinear interpolation. 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

arm_bilinear_interp_f32()

__STATIC_FORCEINLINE float32_t arm_bilinear_interp_f32	(	const arm_bilinear_interp_instance_f32 *	S,
		float32_t	X,
		float32_t	Y
	)

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 6936 of file arm_math.h.

arm_bilinear_interp_q15()

__STATIC_FORCEINLINE q15_t arm_bilinear_interp_q15	(	arm_bilinear_interp_instance_q15 *	S,
		q31_t	X,
		q31_t	Y
	)

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 7075 of file arm_math.h.

arm_bilinear_interp_q31()

__STATIC_FORCEINLINE q31_t arm_bilinear_interp_q31	(	arm_bilinear_interp_instance_q31 *	S,
		q31_t	X,
		q31_t	Y
	)

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 7001 of file arm_math.h.

arm_bilinear_interp_q7()

__STATIC_FORCEINLINE q7_t arm_bilinear_interp_q7	(	arm_bilinear_interp_instance_q7 *	S,
		q31_t	X,
		q31_t	Y
	)

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 7153 of file arm_math.h.