High end processors - impact to video quality

Most audio processors have no video processing 

That's correct.  Most separate "HT Processors" will not have any video processing.  There may be some exceptions, such as Marantz/Yamaha (where their AV receivers use the same HDMI board and may have some video processing/scaling circuits).

That being said, the HDMI video quality between all these devices is not equal.  There may be some processors that output better quality HDMI video.  It all has to do with how they engineered the HDMI board and the power supply lines.  I have found my Krell S1200 has superior HDMI video quality over any other device I have tested.  It's almost like a turbo boost for video.  You can look at the HDMI board and see that there is a large collection of electrolytic power supply filtering caps all around the HDMI IC chips.  It also has several voltage regulators on the board itself. 

If you compare this to a typical receiver, the receiver will NOT have any power supply filtering and all you will see on the HDMI board are the IC chips themselves (along with all the tiny SMD resistors/caps required).

If a receiver/processor does advertise video processing, it is likely a basic color/tint/sharpness adjustment with possibly some noise reduction stuff.  If you really want to look into video processing, check out Lumagen Radiance processors.  Anyone who uses these are typically doing it for real multi-point white balance and color shade correction for the projector itself.  None of the receivers will have anything like this (but it does require additional software and light meters to do the calibration).

@OP  

About Anthem , NAD  and Audio Contol  processors ; you may ask
@audiotroy  .
He carries all those brands.
He surely can give you informations, advices .