This paper presents a technique for determining an object's shape based on the similarity of radiance changes observed at points on its surface under varying illumination. To examine the similarity, we use an observation vector that represents a sequence of pixel intensities of a point on the surface under different lighting conditions. Assuming convex objects under distant illumination and orthographic projection, we show that the similarity between two observation vectors is closely related to the similarity between the surface normals of the corresponding points. This enables us to estimate the object's surface normals solely from the similarity of radiance changes under unknown distant lighting by using dimensionality reduction. Unlike most previous shape reconstruction methods, our technique neither assumes particular reflection models nor requires reference materials. This makes our method applicable to a wide variety of objects made of different materials.