This paper presents a method for visual object recognition based on the linear combination of 2-D images of an object. The approach represents a 3-D object as a linear combination of 2-D images, allowing for the recognition of the object under various transformations, including rigid and non-rigid ones. The method is divided into two parts: first, it shows that different views of the same object can often be expressed as linear combinations of a small number of views. Second, it suggests how this linear combination property can be used in the recognition process. The paper discusses the representation of objects with sharp edges and smooth boundaries. For objects with sharp edges, the linear combination approach is shown to handle rigid transformations and scaling. For objects with smooth boundaries, the method is extended using the curvature method, which predicts the appearance of the object under 3-D rotations. The curvature method is based on the depth and curvature values of the object's contours. The paper also addresses the use of linear combinations for both rigid and non-rigid transformations. It shows that an object undergoing a 3-D rotation can be represented as a linear combination of three images, and that an object undergoing a general 3-D rotation can be represented as a linear combination of five images. The method is further extended to handle translations and scaling, which do not require additional images since they are represented by scaling the coefficients. The paper concludes that the linear combination approach is effective for recognizing objects under various transformations. It is also applicable to non-rigid transformations, such as articulations and non-rigid stretching. The method is implemented and applied to images of 3-D objects, showing good agreement between the actual images and the appropriate linear combinations. The results demonstrate that the linear combination approach is a powerful tool for visual object recognition.This paper presents a method for visual object recognition based on the linear combination of 2-D images of an object. The approach represents a 3-D object as a linear combination of 2-D images, allowing for the recognition of the object under various transformations, including rigid and non-rigid ones. The method is divided into two parts: first, it shows that different views of the same object can often be expressed as linear combinations of a small number of views. Second, it suggests how this linear combination property can be used in the recognition process. The paper discusses the representation of objects with sharp edges and smooth boundaries. For objects with sharp edges, the linear combination approach is shown to handle rigid transformations and scaling. For objects with smooth boundaries, the method is extended using the curvature method, which predicts the appearance of the object under 3-D rotations. The curvature method is based on the depth and curvature values of the object's contours. The paper also addresses the use of linear combinations for both rigid and non-rigid transformations. It shows that an object undergoing a 3-D rotation can be represented as a linear combination of three images, and that an object undergoing a general 3-D rotation can be represented as a linear combination of five images. The method is further extended to handle translations and scaling, which do not require additional images since they are represented by scaling the coefficients. The paper concludes that the linear combination approach is effective for recognizing objects under various transformations. It is also applicable to non-rigid transformations, such as articulations and non-rigid stretching. The method is implemented and applied to images of 3-D objects, showing good agreement between the actual images and the appropriate linear combinations. The results demonstrate that the linear combination approach is a powerful tool for visual object recognition.