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C.11.2.1.3 VOI LUT Function

1. For example, given stored unsigned pixel values from 0 to 65535, a Rescale Intercept (0028,1052) of 0 and a Rescale Slope (0028,1053) of 1.0/65535, a Window Width (0028,1051) of 1.0 and a Window Center (0028,1050) of 0.5 would specify the entire range of values (the identity transformation for those rescale values).

2. Window Width (0028,1051) is required to be greater than zero to prevent division by zero (quite apart from being meaningless).

C.11.2.1.2 Window Center and Window Width

1. For the purpose of this definition, a floating point calculation without integer truncation is assumed, though the manner of implementation may vary as long as the result is the same.

2. The pseudo-code function computes a continuous value over the output range without any discontinuity at the boundaries. The value of 0 for w is expressly forbidden, and the value of 1 for w does not cause division by zero, since the continuous segment of the function will never be reached for that case.

3. For example, for an output range 0 to 255:

   • c=2048, w=4096 becomes:

     • if (x <= 0) then y = 0

     • else if (x > 4095) then y = 255

     • else y = ((x - 2047.5) / 4095 + 0.5) * (255-0) + 0

   • c=2048, w=1 becomes:

     • if (x <= 2047.5) then y = 0

     • else if (x > 2047.5) then y = 255

     • else /* not reached */

   • c=0, w=100 becomes:

     • if (x <= -50) then y = 0

     • else if (x > 49) then y = 255

     • else y = ((x + 0.5) / 99 + 0.5) * (255-0) + 0

   • c=0, w=1 becomes:

     • if (x <= -0.5) then y = 0

     • else if (x > -0.5) then y = 255

     • else /* not reached */

4. A Window Center of 2^n-1 and a Window Width of 2ⁿ selects the range of input values from 0 to 2ⁿ-1. This represents a mathematical identity VOI LUT transformation over the possible input values (whether used or not) in the case where no Modality LUT is specified and the stored pixel data are n bit unsigned integers.

   In the case where x1 is the lowest input value actually used in the Pixel Data and x2 is the highest, a Window Center of (x1+x2+1)/2 and a Window Width of (x2-x1+1) selects the range of input values from x1 to x2, which represents the full range of input values present as opposed to possible. This is distinct from the mathematical identity VOI LUT transformation, which instead selects the full range of input values possible as opposed to those actually used. The mathematical identity and full input range transformations are the same when x1 = 0 and x2 is 2ⁿ-1 and the input values are n bit unsigned integers. See also Note 7.

5. A Window Width of 1 is typically used to represent a "threshold" operation in which those integer input values less than the Window Center are represented as the minimum displayed value and those greater than or equal to the Window Center are represented as the maximum displayed value. A Window Width of 2 will have the same result for integral input values.

6. The application of Window Center (0028,1050) and Window Width (0028,1051) may select a signed input range. There is no implication that this signed input range is clipped to zero.

7. The selected input range may exceed the actual range of the input values, thus effectively "compressing" the contrast range of the displayed data into a narrower band of the available contrast range, and "flattening" the appearance. There are no limits to the maximum value of the window width, or to the minimum or maximum value of window level, both of which may exceed the actual or possible range of input values.

8. Input values "below" the window are displayed as the minimum output value and input values "above" the window are displayed as the maximum output value. This is the common usage of the window operation in medical imaging. There is no provision for an alternative approach in which all values "outside" the window are displayed as the minimum output value.

9. The output of the Window Center/Width or VOI LUT transformation is either implicitly scaled to the full range of the display device if there is no succeeding transformation defined, or implicitly scaled to the full input range of the succeeding transformation step (such as the Presentation LUT), if present. See Section C.11.6.1.

10. Fractional values of Window Center and Window Width are permitted (since the VR of these Attributes is Decimal String), and though they are not often encountered, applications should be prepared to accept them.

1. This requirement is specified so that IODs that define a particular output space for the grayscale pipeline, such as P-Values, are not in an undefined state when no VOI LUT Sequence or Window Width and Window Center are present.

2. Despite the Type 3 requirement for VOI LUT Sequence and Window Center, implementations that render images are expected to implement and apply these transformations when they are present in the image, unless overridden by the user, a presentation state, or a hanging protocol, and to allow the user to select which transformation to apply when multiple transformations are present.