This paper introduces a new method for capturing, representing, and rendering the complete appearance of both synthetic and real-world objects and scenes using a 4D function called a Lumigraph. Unlike traditional shape capture and rendering methods, the Lumigraph does not rely on geometric representations but instead samples and reconstructs a 4D function that describes the flow of light at all positions and directions. This allows for the rapid generation of new images from arbitrary camera positions, independent of the scene's geometric or illumination complexity. The Lumigraph is derived from the plenoptic function, a 5D quantity describing light flow at every 3D spatial position and 2D direction. By restricting the plenoptic function to a surrounding surface (e.g., a cube), the 5D function is reduced to a 4D function. The paper discusses computational methods for capturing and representing this 4D function and using it to render images from any viewpoint. The Lumigraph is represented using a parameterization of a cube with orthogonal axes and a second plane for direction. The 4D function is discretized into a grid of points, with each point associated with a basis function. The basis functions are chosen to ensure computational efficiency and continuity. The Lumigraph is then reconstructed using a combination of sampling, integration, and interpolation techniques. The paper also discusses the use of geometric information to improve the quality of the reconstruction, particularly through depth correction. This involves adjusting the u and v coordinates of the Lumigraph based on the depth of the object's surface. This allows for more accurate interpolation and reduces artifacts in the reconstructed images. The system includes a capture stage where images are taken from multiple viewpoints, followed by processing to create the Lumigraph. The Lumigraph is then used to generate new images using texture mapping and ray tracing. The paper presents results on both synthetic and real-world objects, demonstrating the effectiveness of the Lumigraph in capturing and rendering complex scenes. The system is efficient and can be applied to both synthetic and real-world objects, allowing for the rapid generation of images from any viewpoint. The paper also discusses compression techniques to reduce storage requirements and improve efficiency. The results show that the Lumigraph can be used to create high-quality images with minimal computational overhead.This paper introduces a new method for capturing, representing, and rendering the complete appearance of both synthetic and real-world objects and scenes using a 4D function called a Lumigraph. Unlike traditional shape capture and rendering methods, the Lumigraph does not rely on geometric representations but instead samples and reconstructs a 4D function that describes the flow of light at all positions and directions. This allows for the rapid generation of new images from arbitrary camera positions, independent of the scene's geometric or illumination complexity. The Lumigraph is derived from the plenoptic function, a 5D quantity describing light flow at every 3D spatial position and 2D direction. By restricting the plenoptic function to a surrounding surface (e.g., a cube), the 5D function is reduced to a 4D function. The paper discusses computational methods for capturing and representing this 4D function and using it to render images from any viewpoint. The Lumigraph is represented using a parameterization of a cube with orthogonal axes and a second plane for direction. The 4D function is discretized into a grid of points, with each point associated with a basis function. The basis functions are chosen to ensure computational efficiency and continuity. The Lumigraph is then reconstructed using a combination of sampling, integration, and interpolation techniques. The paper also discusses the use of geometric information to improve the quality of the reconstruction, particularly through depth correction. This involves adjusting the u and v coordinates of the Lumigraph based on the depth of the object's surface. This allows for more accurate interpolation and reduces artifacts in the reconstructed images. The system includes a capture stage where images are taken from multiple viewpoints, followed by processing to create the Lumigraph. The Lumigraph is then used to generate new images using texture mapping and ray tracing. The paper presents results on both synthetic and real-world objects, demonstrating the effectiveness of the Lumigraph in capturing and rendering complex scenes. The system is efficient and can be applied to both synthetic and real-world objects, allowing for the rapid generation of images from any viewpoint. The paper also discusses compression techniques to reduce storage requirements and improve efficiency. The results show that the Lumigraph can be used to create high-quality images with minimal computational overhead.