Perpendicular Vegetation Index (PVI)

"The Perpendicular Vegetation Index (PVI) is similar to a difference vegetation index; however, it is sensitive to atmospheric variations. When using this method to compare different images, it should only be used on images that have been atmospherically corrected.

PVI=(NIR-a*Red-b)/(sqrt(1+a2))

    NIR = pixel values from the near-infrared band
    Red = pixel values from the red band
    a = slope of the soil line
    b = gradient of the soil line

This index outputs values between -1.0 and 1.0." (ESRI, 2018)