The paper presents a novel algorithm for deformable shape matching and object recognition, focusing on finding correspondences between feature points in images. The algorithm formulates the correspondence problem as an integer quadratic programming (IQP) problem, where the cost function includes terms based on the similarity of geometric blur point descriptors and the geometric distortion between corresponding feature points. The method handles outliers and occlusions, enabling accurate matching even in cluttered scenes. Given the correspondences, a regularized thin plate spline is used to estimate an aligning transform, resulting in dense correspondences between two shapes. Object recognition is then performed using a nearest neighbor framework, where the distance between exemplars and queries is the matching cost between corresponding points. The approach is evaluated on the Caltech 101 dataset and face detection tasks, achieving 48% correct classification rate and competitive results in face localization, respectively. The paper also discusses related work, introduces the geometric blur descriptor, and details the correspondence algorithm and its approximation techniques.The paper presents a novel algorithm for deformable shape matching and object recognition, focusing on finding correspondences between feature points in images. The algorithm formulates the correspondence problem as an integer quadratic programming (IQP) problem, where the cost function includes terms based on the similarity of geometric blur point descriptors and the geometric distortion between corresponding feature points. The method handles outliers and occlusions, enabling accurate matching even in cluttered scenes. Given the correspondences, a regularized thin plate spline is used to estimate an aligning transform, resulting in dense correspondences between two shapes. Object recognition is then performed using a nearest neighbor framework, where the distance between exemplars and queries is the matching cost between corresponding points. The approach is evaluated on the Caltech 101 dataset and face detection tasks, achieving 48% correct classification rate and competitive results in face localization, respectively. The paper also discusses related work, introduces the geometric blur descriptor, and details the correspondence algorithm and its approximation techniques.