The fashion industry's latest hope for protecting its designs may hang on a slimming pair of yoga pants.

Yoga-apparel maker Lululemon Athletica Inc. is accusing fashion house Calvin Klein Inc. of infringing on design patents for its popular $98 "Astro Pant" in a legal battle that could provide new ammunition for the industry to wield against copycats while bolstering Lululemon's dominant position in high-end yoga apparel.

Lululemon,...