You may have seen the Color Palette Generators online. They are loads of fun and the palettes they generate can be lovely (or terrifying). If you have a special piece of art in your home and want to use the colors to influence your interior space, you may either take a photo (get the best quality you can, then crop it down) and upload it to any one of those generators. Sherwin Williams offers one called "Color Snap", and while I like that it offers me actual paint colors, I would not suggest trusting this entirely. Colors perception is not 100% intelligent from a photograph or online image.
Woohoo! I have a palette. Time to buy the paint, right?
Wrong. Now that you have the color names, and possibly paint swatches. Compare them to your art. Do the swatches complement the art? Clash? Time to refine that selection to ensure a proper match or complementing hues.
Everything looks good, now can I buy my paint?
Wait... who said anything about paint? No, seriously. This color palette should not just be paint colors. Use these colors in selecting fabrics and other finishes. Consider the feeling these colors provide when you choose that table lamp that you've been needing. In a well designed home, everything affects everything else. And, sometimes the fact that they are so different is what is considered! Confusing? Yup, sorry.
So, use this as a basis, a feeling. But, you want to hear a real secret? Your art does not need to "match" your space! Art should be art, and yes it should be selected carefully as the size and placement are crucial for proper viewing, but does the art need to match the museum? Nope. And, art does not need to match your home- you just need to love it.
Now, go have fun with your palettes!