How would I go about creating an effect such as the people in this image. I like the simplicity of only a few colors and shapes. Is there a filter I could use?
Bitmap filters will likely not give us the desired result here. Depending on the bitmap source we may however very quickly get rather good results after tracing a bitmap to vector graphics (below image processing took me just a minute).
In this case I took a random picture from the web to import it as bitmap in Inkscape (but any other vector oriented graphics application will do this too). In Inkscape we have the option "Path - Trace Bitmap..." to convert the bitmap to vector objects. In the above example I simply created a stacked group of 8 colors with smooth outlines.
Outcome depends mostly on the number of color steps with fewer colors resulting in a more flat picture.
The advantage of this approach is that we can easily change the color of each color path from the object's properties. We may also add a stroke pattern to outline color borders or further fine tune the object's shapes (e.g. remove the white spot on the boy's cheek).
Short answer: No.
These are illustrations and there is simply no push-button solution for it. Also because it depends heavily on the image materials.
There are two things you can do. One is playing with various filters and contrast in photoshop till you get the desired effect and the other is tracing the shapes with the pen tool (AI or PSD). Either way, it's a lot of work to get it right.