This paper presents a spectral method for finding consistent correspondences between two sets of features using pairwise constraints. The method constructs an adjacency matrix M where nodes represent potential correspondences and edge weights represent pairwise agreement between them. Correct assignments are likely to form a strongly connected cluster, while incorrect ones are unlikely to. The principal eigenvector of M is used to identify the main cluster, and the mapping constraints are applied to determine the correct assignments. The method is robust to outliers, accurate in matching rate, and significantly faster than existing methods. The approach is based on the observation that the graph associated with M contains a main strongly connected cluster formed by correct assignments and many incorrect assignments outside or weakly connected to it. The method uses the principal eigenvector of M to determine the association of each assignment with the main cluster. Assignments with low association are rejected until the mapping constraints are satisfied. The algorithm is a greedy approach that starts with the assignment with the highest confidence and iteratively rejects conflicting assignments. The process continues until all assignments are either accepted or rejected. The method is efficient and robust to noise and outliers, and it scales well to large datasets. The method is tested on various tasks, including matching 2D points with white noise, non-rigid deformations using the Thin Plate Spline model, and recognizing objects from low-resolution images. The results show that the method is robust to noise and outliers, and it outperforms existing methods in terms of speed and accuracy. The method is also effective in recognizing vehicles from aerial images using SIFT descriptors. The paper concludes that the spectral approach is efficient and robust for correspondence problems, and it can be applied to a variety of vision tasks.This paper presents a spectral method for finding consistent correspondences between two sets of features using pairwise constraints. The method constructs an adjacency matrix M where nodes represent potential correspondences and edge weights represent pairwise agreement between them. Correct assignments are likely to form a strongly connected cluster, while incorrect ones are unlikely to. The principal eigenvector of M is used to identify the main cluster, and the mapping constraints are applied to determine the correct assignments. The method is robust to outliers, accurate in matching rate, and significantly faster than existing methods. The approach is based on the observation that the graph associated with M contains a main strongly connected cluster formed by correct assignments and many incorrect assignments outside or weakly connected to it. The method uses the principal eigenvector of M to determine the association of each assignment with the main cluster. Assignments with low association are rejected until the mapping constraints are satisfied. The algorithm is a greedy approach that starts with the assignment with the highest confidence and iteratively rejects conflicting assignments. The process continues until all assignments are either accepted or rejected. The method is efficient and robust to noise and outliers, and it scales well to large datasets. The method is tested on various tasks, including matching 2D points with white noise, non-rigid deformations using the Thin Plate Spline model, and recognizing objects from low-resolution images. The results show that the method is robust to noise and outliers, and it outperforms existing methods in terms of speed and accuracy. The method is also effective in recognizing vehicles from aerial images using SIFT descriptors. The paper concludes that the spectral approach is efficient and robust for correspondence problems, and it can be applied to a variety of vision tasks.