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/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_bilinear_interp_f32.c
* Description: Floating-point bilinear interpolation
*
* $Date: 23 April 2021
* $Revision: V1.9.0
*
* Target Processor: Cortex-M and Cortex-A cores
* -------------------------------------------------------------------- */
/*
* Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved.
*
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an AS IS BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "dsp/interpolation_functions.h"
/**
@ingroup groupInterpolation
*/
/**
* @defgroup BilinearInterpolate Bilinear Interpolation
*
* Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.
* The underlying function <code>f(x, y)</code> 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.
*
* <b>Algorithm</b>
* \par
* The instance structure used by the bilinear interpolation functions describes a two dimensional data table.
* For floating-point, the instance structure is defined as:
* <pre>
* typedef struct
* {
* uint16_t numRows;
* uint16_t numCols;
* float32_t *pData;
* } arm_bilinear_interp_instance_f32;
* </pre>
*
* \par
* where <code>numRows</code> specifies the number of rows in the table;
* <code>numCols</code> specifies the number of columns in the table;
* and <code>pData</code> points to an array of size <code>numRows*numCols</code> values.
* The data table <code>pTable</code> is organized in row order and the supplied data values fall on integer indexes.
* That is, table element (x,y) is located at <code>pTable[x + y*numCols]</code> where x and y are integers.
*
* \par
* Let <code>(x, y)</code> specify the desired interpolation point. Then define:
* <pre>
* XF = floor(x)
* YF = floor(y)
* </pre>
* \par
* The interpolated output point is computed as:
* <pre>
* 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)
* </pre>
* 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.
*
* \par
* if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output.
*/
/**
* @addtogroup BilinearInterpolate
* @{
*/
/**
* @brief Floating-point bilinear interpolation.
* @param[in,out] S points to an instance of the interpolation structure.
* @param[in] X interpolation coordinate.
* @param[in] Y interpolation coordinate.
* @return out interpolated value.
*/
float32_t arm_bilinear_interp_f32(
const arm_bilinear_interp_instance_f32 * S,
float32_t X,
float32_t Y)
{
float32_t out;
float32_t f00, f01, f10, f11;
float32_t *pData = S->pData;
int32_t xIndex, yIndex, index;
float32_t xdiff, ydiff;
float32_t b1, b2, b3, b4;
xIndex = (int32_t) X;
yIndex = (int32_t) Y;
/* Care taken for table outside boundary */
/* Returns zero output when values are outside table boundary */
if (xIndex < 0 || xIndex > (S->numCols - 2) || yIndex < 0 || yIndex > (S->numRows - 2))
{
return (0);
}
/* Calculation of index for two nearest points in X-direction */
index = (xIndex ) + (yIndex ) * S->numCols;
/* Read two nearest points in X-direction */
f00 = pData[index];
f01 = pData[index + 1];
/* Calculation of index for two nearest points in Y-direction */
index = (xIndex ) + (yIndex+1) * S->numCols;
/* Read two nearest points in Y-direction */
f10 = pData[index];
f11 = pData[index + 1];
/* Calculation of intermediate values */
b1 = f00;
b2 = f01 - f00;
b3 = f10 - f00;
b4 = f00 - f01 - f10 + f11;
/* Calculation of fractional part in X */
xdiff = X - xIndex;
/* Calculation of fractional part in Y */
ydiff = Y - yIndex;
/* Calculation of bi-linear interpolated output */
out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;
/* return to application */
return (out);
}
/**
* @} end of BilinearInterpolate group
*/
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