Correspondence Networks with Adaptive Neighbourhood Consensus

In this paper, we tackle the task of establishing dense visual correspondences between images containing objects of the same category. This is a challenging task due to large intra-class variations and a lack of dense pixel level annotations. We propose a convolutional neural network architecture, called adaptive neighbourhood consensus network (ANC-Net), that can be trained end-to-end with sparse key-point annotations, to handle this challenge. At the core of ANC-Net is our proposed non-isotropic 4D convolution kernel, which forms the building block for the adaptive neighbourhood consensus module for robust matching. We also introduce a simple and efficient multi-scale self-similarity module in ANC-Net to make the learned feature robust to intra-class variations. Furthermore, we propose a novel orthogonal loss that can enforce the one-to-one matching constraint. We thoroughly evaluate the effectiveness of our method on various benchmarks, where it substantially outperforms state-of-the-art methods.Comment: CVPR 2020. Project page: https://ancnet.avlcode.org

Error bound and exact penalty method for optimization problems with nonnegative orthogonal constraint

This paper is concerned with a class of optimization problems with the nonnegative orthogonal constraint, in which the objective function is $L$-smooth on an open set containing the Stiefel manifold ${\rm St}(n,r)$. We derive a locally Lipschitzian error bound for the feasible points without zero rows when $n>r>1$, and when $n>r=1$ or $n=r$ achieve a global Lipschitzian error bound. Then, we show that the penalty problem induced by the elementwise $\ell_1$-norm distance to the nonnegative cone is a global exact penalty, and so is the one induced by its Moreau envelope under a lower second-order calmness of the objective function. A practical penalty algorithm is developed by solving approximately a series of smooth penalty problems with a retraction-based nonmonotone line-search proximal gradient method, and any cluster point of the generated sequence is shown to be a stationary point of the original problem. Numerical comparisons with the ALM \citep{Wen13} and the exact penalty method \citep{JiangM22} indicate that our penalty method has an advantage in terms of the quality of solutions despite taking a little more time.Comment: 34 pages, and 6 figure

Nonnegative Orthogonal Graph Matching

Graph matching problem that incorporates pair-wise constraints can be formulated as Quadratic Assignment Problem(QAP). The optimal solution of QAP is discrete and combinational, which makes QAP problem NP-hard. Thus, many algorithms have been proposed to find approximate solutions. In this paper, we propose a new algorithm, called Nonnegative Orthogonal Graph Matching (NOGM), for QAP matching problem. NOGM is motivated by our new observation that the discrete mapping constraint of QAP can be equivalently encoded by a nonnegative orthogonal constraint which is much easier to implement computationally. Based on this observation, we develop an effective multiplicative update algorithm to solve NOGM and thus can find an effective approximate solution for QAP problem. Comparing with many traditional continuous methods which usually obtain continuous solutions and should be further discretized, NOGM can obtain a sparse solution and thus incorporates the desirable discrete constraint naturally in its optimization. Promising experimental results demonstrate benefits of NOGM algorithm