This paper presents a method for shape matching and object recognition using low distortion correspondences. The approach is based on finding correspondences between feature points in a model and a query image, which is formulated as an integer quadratic programming problem. The cost function includes terms for the similarity of geometric blur descriptors and the geometric distortion between corresponding points. The algorithm handles outliers and enables matching in the presence of occlusion and clutter. After finding correspondences, a regularized thin plate spline is used to estimate an aligning transform, resulting in a dense correspondence between the two shapes. Object recognition is performed using a nearest neighbor framework, where the distance between exemplars and queries is based on the matching cost between corresponding points. The method is tested on two datasets: the Caltech 101 dataset, which contains 101 object categories with significant intra-class variation, and a dataset of news photographs containing faces. On the Caltech 101 dataset, the method achieves a 48% correct classification rate, compared to 16% from previous methods. For face detection, the method performs comparably to specialized face detectors. The paper also introduces a geometric blur descriptor, which is a smoothed version of the signal around a feature point, blurred by a spatially varying kernel. This descriptor is used to capture discriminative information while being robust to geometric distortion. The method also considers geometric distortion costs, which are used to penalize changes in direction and length between corresponding points. The correspondence algorithm is formulated as an integer quadratic programming problem, which is approximated using a two-step process involving linear bounding and gradient descent. The algorithm is tested on various datasets and is shown to be effective in handling occlusion, clutter, and scale variation. The results demonstrate that the method provides accurate object recognition and localization, with performance comparable to state-of-the-art methods.This paper presents a method for shape matching and object recognition using low distortion correspondences. The approach is based on finding correspondences between feature points in a model and a query image, which is formulated as an integer quadratic programming problem. The cost function includes terms for the similarity of geometric blur descriptors and the geometric distortion between corresponding points. The algorithm handles outliers and enables matching in the presence of occlusion and clutter. After finding correspondences, a regularized thin plate spline is used to estimate an aligning transform, resulting in a dense correspondence between the two shapes. Object recognition is performed using a nearest neighbor framework, where the distance between exemplars and queries is based on the matching cost between corresponding points. The method is tested on two datasets: the Caltech 101 dataset, which contains 101 object categories with significant intra-class variation, and a dataset of news photographs containing faces. On the Caltech 101 dataset, the method achieves a 48% correct classification rate, compared to 16% from previous methods. For face detection, the method performs comparably to specialized face detectors. The paper also introduces a geometric blur descriptor, which is a smoothed version of the signal around a feature point, blurred by a spatially varying kernel. This descriptor is used to capture discriminative information while being robust to geometric distortion. The method also considers geometric distortion costs, which are used to penalize changes in direction and length between corresponding points. The correspondence algorithm is formulated as an integer quadratic programming problem, which is approximated using a two-step process involving linear bounding and gradient descent. The algorithm is tested on various datasets and is shown to be effective in handling occlusion, clutter, and scale variation. The results demonstrate that the method provides accurate object recognition and localization, with performance comparable to state-of-the-art methods.