Operator Library: Arithmetics
The operator calculates the arctan of the input.
The input range of arctan is [∞, ∞]. This operator includes a parameter Resolution to define the fixed point resolution bits of the input values. The input range is given by the number of input bits =
![](../../images/math/math-snippet-362.png)
where
![](../../images/math/math-snippet-363.png)
is the bit width at the input and R the resolution bits.
The argument x of the arctan function is determined by
![](../../images/math/math-snippet-364.png)
The results of the arctan function are in the range ]- π/2, π/2[. The output value range of the operator in VisualApplets is mapped to
![](../../images/math/math-snippet-365.png)
where
![](../../images/math/math-snippet-366.png)
is the bit width at the output link. Thus the output value is
![](../../images/math/math-snippet-367.png)
The following image shows the plot of the arctan function.
![](../../images/library/Arithmetics/arctan.png)
In the next figure, the VisualApplets operator implementation is shown. Note the input and output bit widths.
![](../../images/library/Arithmetics/arctan_implementation.png)
Le't have a look at an input pixel value. For example -50. With the given resolution of four, the real value representation of the pixel value is -50/16. The arctan result of -50/16 is arctan(-50/16) = -1.26. In pixel value representation this result becomes -51,38 which is the same as shown in the plot.
Link Parameter | Input Link I | Output Link O |
---|---|---|
Bit Width | [8, 12] | [8,32] |
Arithmetic | signed | signed |
Parallelism | any | as I |
Kernel Columns | 1 | as I |
Kernel Rows | 1 | as I |
Img Protocol | {VALT_IMAGE2D, VALT_LINE1D, VALT_PIXEL0D} | as I |
Color Format | VAF_GRAY | as I |
Color Flavor | FL_NONE | as I |
Max. Img Width | any | as I |
Max. Img Height | any | as I |
ResolutionBits | |
---|---|
Type | static parameter |
Default | 8 |
Range | [0, OutputBitWidth] |
This parameter defines the accuracy of the input values as defined in the description above. |
The use of operator ARCTAN is shown in the following examples:
-
Example - Calculates image moments orientation and eccentricity
-
'Histogram of Oriented Gradients (HOG)'
Examples- Histogram of oriented Gradients
-
'Functional Example for Specific Operators of Library Arithmentics: Trigonometric Functions'
Examples - Demonstration of how to use the operator