To clarify: you want an area of the desktop, not just within the bounds of your window, to be under your control allowing you to apply a per-pixel filter. If that's the case, I think what you need is DirectDraw using the XNA libraries. WPF MAY get you what you need, but WinForms will most likely not. There are third party tools as well.
If you want this capability only within the bounds of your application's window, for instance in a drawing application, it gets far easier. Every class in the Windows.Forms namespace that inherits from Control exposes a CreateGraphics() method. This method returns an object representing a drawing surface covering the screen area of the control, and is the basis for just about anything you want to do on a window involving custom graphics (and internally, it's used to draw the controls in the first place).
Once you have the Graphics object, you can draw Images on it. A popular method of drawing custom graphics like animations or games is to do the actual drawing on a Bitmap object (derived from the abstract Image) and then when you're done, draw the Bitmap on the Graphics area. This is done to reduce flicker; if the graphics area is shown to the user while it is being drawn on, the user will only see the complete image for a split second before it is "wiped" and redrawn, and shapes drawn halfway through will be there one moment and gone the next as they wait to be drawn. Drawing to a bitmap, then showing the Bitmap on the screen when you're done, means the user sees a complete image at a time.
You can extend this using transparency features to create multi-layered images. Have a Bitmap for every layer you wish to manipulate. Work on them seperately, then draw each of them, in their proper order from back to front, onto a master Bitmap, and draw that Bitmap on the screen. This allows you those PhotoShop-type manipulations where a part of the image is one layer, and can be manipulated independently of all others.
As for per-pixel filtering, Bitmap objects expose GetPixel() and SetPixel() methods, which allow you to grab the color of a single pixel, perform a filter calculation, and re-draw it. This process will be totally unaccelerated, and so limited by your CPU speed, but allow very fine control of your image, or repetitive tasks like your filters.