The MitchellâNetravali filters or BC-splines are a group of reconstruction filters used primarily in computer graphics, which can be used, for example, for anti-aliasing or for scaling raster graphics. They are also known as bicubic filters in image editing programs because they are bi-dimensional cubic splines. [1] [2] [3]
The MitchellâNetravali filters were designed as part of an investigation into artifacts from reconstruction filters. The filters are piece-wise cubic filters with four-pixel wide supports. After excluding unsuitable filters from this family, such as discontinuous curves, two parameters and remain, through which the MitchellâNetravali filters can be configured. The filters are defined as follows:
It is possible to construct two-dimensional versions of the MitchellâNetravali filters by separation. In this case the filters can be replaced by a series of interpolations with the one-dimensional filter. From the color values of the four neighboring pixels , , , the color value is then calculated as follows:
lies between and ; is the distance between and .
Various artifacts may result from certain choices of parameters B and C, as shown in the following illustration. The researchers recommended values from the family (dashed line) and especially as a satisfactory compromise. [1] [4]
The following parameters result in well-known cubic splines used in common image editing programs:
B | C | Cubic spline | Common implementations |
---|---|---|---|
0 | Any | Cardinal splines | |
0 | 0.5 | Catmull-Rom spline | Bicubic filter in GIMP |
0 | 0.75 | Unnamed | Bicubic filter in Adobe Photoshop [5] |
1/3 | 1/3 | MitchellâNetravali | Mitchell filter in ImageMagick [4] |
1 | 0 | B-spline | Bicubic filter in Paint.net |
The MitchellâNetravali filters or BC-splines are a group of reconstruction filters used primarily in computer graphics, which can be used, for example, for anti-aliasing or for scaling raster graphics. They are also known as bicubic filters in image editing programs because they are bi-dimensional cubic splines. [1] [2] [3]
The MitchellâNetravali filters were designed as part of an investigation into artifacts from reconstruction filters. The filters are piece-wise cubic filters with four-pixel wide supports. After excluding unsuitable filters from this family, such as discontinuous curves, two parameters and remain, through which the MitchellâNetravali filters can be configured. The filters are defined as follows:
It is possible to construct two-dimensional versions of the MitchellâNetravali filters by separation. In this case the filters can be replaced by a series of interpolations with the one-dimensional filter. From the color values of the four neighboring pixels , , , the color value is then calculated as follows:
lies between and ; is the distance between and .
Various artifacts may result from certain choices of parameters B and C, as shown in the following illustration. The researchers recommended values from the family (dashed line) and especially as a satisfactory compromise. [1] [4]
The following parameters result in well-known cubic splines used in common image editing programs:
B | C | Cubic spline | Common implementations |
---|---|---|---|
0 | Any | Cardinal splines | |
0 | 0.5 | Catmull-Rom spline | Bicubic filter in GIMP |
0 | 0.75 | Unnamed | Bicubic filter in Adobe Photoshop [5] |
1/3 | 1/3 | MitchellâNetravali | Mitchell filter in ImageMagick [4] |
1 | 0 | B-spline | Bicubic filter in Paint.net |