Despite its significant progress, cross-modal retrieval still suffers from one-to-many matching cases, where the multiplicity of semantic instances in another modality could be acquired by a given query. However, existing approaches usually map heterogeneous data into the learned space as deterministic point vectors. In spite of their remarkable performance in matching the most similar instance, such deterministic point embedding suffers from the insufficient representation of rich semantics in one-to-many correspondence. To address the limitations, we intuitively extend a deterministic point into a closed geometry and develop geometric representation learning methods for cross-modal retrieval. Thus, a set of points inside such a geometry could be semantically related to many candidates, and we could effectively capture the semantic uncertainty. We then introduce two types of geometric matching for one-to-many correspondence, i.e., point-to-rectangle matching (dubbed P2RM) and rectangle-to-rectangle matching (termed R2RM). The former treats all retrieved candidates as rectangles with zero volume (equivalent to points) and the query as a box, while the latter encodes all heterogeneous data into rectangles. Therefore, we could evaluate semantic similarity among heterogeneous data by the Euclidean distance from a point to a rectangle or the volume of intersection between two rectangles. Additionally, both strategies could be easily employed for off-the-self approaches and further improve the retrieval performance of baselines. Under various evaluation metrics, extensive experiments and ablation studies on several commonly used datasets, two for image-text matching and two for video-text retrieval, demonstrate our effectiveness and superiority.

Based on deterministic single-point embedding, most extant image-text retrieval methods only focus on the match of ground truth while suffering from one-to-many correspondence, where besides annotated positives, many similar instances of another modality should be retrieved by a given query. Recent solutions of probabilistic embedding and rectangle mapping still encounter some drawbacks, albeit their promising effectiveness at multiple matches. Meanwhile, the exploration of one-to-many correspondence is still insufficient. Therefore, this paper proposes a novel geometric representation toEstimate theSemantics of heterogeneous data viaSectorEmbedding (dubbed ESSE). Specifically, a given image/text can be projected as a sector, where its symmetric axis represents mean semantics and the aperture estimates uncertainty. Further, a sector matching loss is introduced to better handle the multiplicity by considering the sine of included angles as distance calculation, which encourages candidates to be contained by the apertures of a query sector. The experimental results on three widely used benchmarks CUB, Flickr30K and MS-COCO reveal that sector embedding can achieve competitive performance on multiple matches and also improve the traditional ground-truth matching of the baselines. Additionally, we also verify the generalization to video-text retrieval on two extensively used datasets of MSRVTT and MSVD, and to text-based person retrieval on CUHK-PEDES. This superiority and effectiveness can also demonstrate that the bounded property of the aperture can better estimate semantic uncertainty when compared to prior remedies.

Image-text retrieval is a fundamental task to bridge vision and language by exploiting various strategies to finegrained alignment between regions and words. This is still tough mainly because of one-to-many correspondence, where a set of matches from another modality can be accessed by a random query. While existing solutions to this problem including multi-point mapping, probabilistic distribution, and geometric embedding have made promising progress, one-to-many correspondence is still under-explored. In this work, we develop a Multilateral Semantic Relations Modeling (termed MSRM) for image-text retrieval to capture the one-to-many correspondence between multiple samples and a given query via hypergraph modeling. Specifically, a given query is first mapped as a probabilistic embedding to learn its true semantic distribution based on Mahalanobis distance. Then each candidate instance in a mini-batch is regarded as a hypergraph node with its mean semantics while a Gaussian query is modeled as a hyperedge to capture the semantic correlations beyond the pair between candidate points and the query. Comprehensive experimental results on two widely used datasets demonstrate that our MSRM method can outper-form state-of-the-art methods in the settlement of multiple matches while still maintaining the comparable performance of instance-level matching.

Deep Metric Learning (DML) is very effective for many computer vision applications such as image retrieval or cross-modal matching. The common paradigm for DML is to seek metric spaces that can encode semantically similar objects close while locating the dissimilar ones far away from each other. To make features more discriminative, the mainstream methods usually design various specific loss functions to seek the help of hard negatives through complex hard mining strategies or hard synthesizing with additional networks. In spite of their fruitfulness, these approaches ignore the impact of low-level information in images on the performance, which may degrade the discerning ability of learned embedding. To alleviate these problems, we introduce a simple yet effective augmentation method to generate more hard negatives by swapping the low-frequency spectra of negative instances with anchors in the Fourier domain. Specifically, unlike previous methods, our proposed approach does not involve any complex design strategies but enriches hard negatives by manipulating the low-level variability of images only with simple Fourier transforms. In addition, our method is treated as a universal plug-in, which can be incorporated into different models for performance improvement. In the end, we conduct extensive experiments to evaluate our method on the widely-used datasets including CUB-200–2011, CARS-196, and Stanford Online Products. Our quantitative results demonstrate that the proposed plug-in outperforms previous approaches consistently and significantly across different datasets and evaluation metrics.

The difficulty of image-text retrieval is further exacerbated by the phenomenon of one-to-many correspondence, where multiple semantic manifestations of the other modality could be obtained by a given query. However, the prevailing methods adopt the deterministic embedding strategy to retrieve the most similar candidate, which encodes the representations of different modalities as single points in vector space. We argue that such a deterministic point mapping is obviously insufficient to represent a potential set of retrieval results for one-to-many correspondence, despite its noticeable progress. As a remedy to this issue, we propose a Point to Rectangle Matching (abbreviated as P2RM) mechanism, which actually is a geometric representation learning method for image-text retrieval. Specifically, our intuitive insight is that the representations of different modalities could be extended to rectangles, then a set of points inside such a rectangle embedding could be semantically related to many candidate correspondences. Thus our P2RM method could essentially address the one-to-many correspondence. Besides, we design a novel semantic similarity measurement method from the perspective of distance for our rectangle embedding. Under the evaluation metric for multiple matches, extensive experiments and ablation studies on two commonly used benchmarks demonstrate our effectiveness and superiority in tackling the multiplicity of image-text retrieval.