“Output” Processing Tab
The contrast filters (curves, gamma compensation, sigmoidal contrast) on this tab are always applied to your image, also when the tab preview for another tab is enabled.
Background: During the processing of this tab the color space conversion from linear RGB to the preview or output profile is calculated. So, in most cases the image will be transformed to sRGB. With this transformation the image gets a lot brighter (you don't see this in Photivo) since the gamma curve of sRGB is applied. However, many people consider the result of this gamma curve unpleasant, so most other programs apply additional contrast to the image.
Photivo offers several possibilities: the two curves (e.g. to load a camera or purpose specific curve), the gamma compensation (like UFRaw) and sigmodial contrast. Those contrast adjustments are meant to stay fixed within reasonable bounds, e.g. if you always shoot landscape it shouldn't change. Of course, when your next assignment is a wedding with harsh contrasts, it may well change for that purpose… So, it's recommmended that you settle for an appearance you like and don't use these filters for creative purposes. However, it's a free world
The base curve is a regular RGB curve on linear RGB data (like the one on the RGB tab). It is just called base curve to emphasize its purpose for general tone adjustment, e.g. it sets the base tone of the camera.