Speeded-up, relaxed spatial matching

A wide range of properties and assumptions determine the most appropriate spatial matching model for an application, e.g. recognition, detection, registration, or large scale image retrieval. Most notably, these include discriminative power, geometric invariance, rigidity constraints, mapping constraints, assumptions made on the underlying features or descriptors and, of course, computational complexity. Having image retrieval in mind, we present a very simple model inspired by Hough voting in the transformation space, where votes arise from single feature correspondences. A relaxed matching process allows for multiple matching surfaces or non-rigid objects under one-to-one mapping, yet is linear in the number of correspondences. We apply it to geometry re-ranking in a search engine, yielding superior performance with the same space requirements but a dramatic speed-up compared to the state of the art.

Related papers:

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title: Distinctive Image Features from Scale-Invariant Keypoints
abstract: The Scale-Invariant Feature Transform (or SIFT) algorithm is a highly robust method to extract and consequently match distinctive invariant features from images. These features can then be used to reliably match objects in diering images. The algorithm was rst proposed by Lowe  and further developed to increase performance resulting in the classic paper [13] that served as foundation for SIFT which has played an important role in robotic and machine vision in the past decade.

title: A spectral technique for correspondence problems using pairwise constraints
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title: The Pyramid Match Kernel: Efficient Learning with Sets of Features
abstract: In numerous domains it is useful to represent a single example by the set of the local features or parts that comprise it. However, this representation poses a challenge to many conventional machine learning techniques, since sets may vary in cardinality and elements lack a meaningful ordering. Kernel methods can learn complex functions, but a kernel over unordered set inputs must somehow solve for correspondences---generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function called the pyramid match that measures partial match similarity in time linear in the number of features. The pyramid match maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in order to find implicit correspondences based on the finest resolution histogram cell where a matched pair first appears. We show the pyramid match yields a Mercer kernel, and we prove bounds on its error relative to the optimal partial matching cost. We demonstrate our algorithm on both classification and regression tasks, including object recognition, 3-D human pose inference, and time of publication estimation for documents, and we show that the proposed method is accurate and significantly more efficient than current approaches.

title: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography
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title: Flexible Spatial Configuration of Local Image Features
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title: Lost in quantization: Improving particular object retrieval in large scale image databases
abstract: The state of the art in visual object retrieval from large databases is achieved by systems that are inspired by text retrieval. A key component of these approaches is that local regions of images are characterized using high-dimensional descriptors which are then mapped to ldquovisual wordsrdquo selected from a discrete vocabulary.This paper explores techniques to map each visual region to a weighted set of words, allowing the inclusion of features which were lost in the quantization stage of previous systems. The set of visual words is obtained by selecting words based on proximity in descriptor space. We describe how this representation may be incorporated into a standard tf-idf architecture, and how spatial verification is modified in the case of this soft-assignment. We evaluate our method on the standard Oxford Buildings dataset, and introduce a new dataset for evaluation. Our results exceed the current state of the art retrieval performance on these datasets, particularly on queries with poor initial recall where techniques like query expansion suffer. Overall we show that soft-assignment is always beneficial for retrieval with large vocabularies, at a cost of increased storage requirements for the index.

title: Relaxed matching kernels for robust image comparison
abstract: The popular bag-of-features representation for object recognition collects signatures of local image patches and discards spatial information. Some have recently attempted to at least partially overcome this limitation, for instance by ldquospatial pyramidsrdquo and ldquoproximityrdquo kernels. We introduce the general formalism of ldquorelaxed matching kernelsrdquo (RMKs) that includes such approaches as special cases, allow us to derive useful general properties of these kernels, and to introduce new ones. As an example, we introduce a kernel based on matching graphs of features and one based on matching information-compressed features. We show that all RMKs are competitive and outperform in several cases recently published state-of-the-art results on standard datasets. However, we also show that a proper implementation of a baseline bag-of-features algorithm can be extremely competitive, and outperform the other methods in some cases.

title: Quick Shift and Kernel Methods for Mode Seeking
abstract: We show that the complexity of the recently introduced medoid-shift algorithm in clustering N points is O(N 2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then exploit kernel methods to extend both mean shift and the improved medoid shift to a large family of distances, with complexity bounded by the effective rank of the resulting kernel matrix, and with explicit regularization constraints. Finally, we show that, under certain conditions, medoid shift fails to cluster data points belonging to the same mode, resulting in over-fragmentation. We propose remedies for this problem, by introducing a novel, simple and extremely efficient clustering algorithm, called quick shift, that explicitly trades off under- and over-fragmentation. Like medoid shift, quick shift operates in non-Euclidean spaces in a straightforward manner. We also show that the accelerated medoid shift can be used to initialize mean shift for increased efficiency. We illustrate our algorithms to clustering data on manifolds, image segmentation, and the automatic discovery of visual categories.

title: Total Recall: Automatic Query Expansion with a Generative Feature Model for Object Retrieval
abstract: Given a query image of an object, our objective is to retrieve all instances of that object in a large (1M+) image database. We adopt the bag-of-visual-words architecture which has proven successful in achieving high precision at low recall. Unfortunately, feature detection and quantization are noisy processes and this can result in variation in the particular visual words that appear in different images of the same object, leading to missed results. In the text retrieval literature a standard method for improving performance is query expansion. A number of the highly ranked documents from the original query are reissued as a new query. In this way, additional relevant terms can be added to the query. This is a form of blind rele- vance feedback and it can fail if 'outlier' (false positive) documents are included in the reissued query. In this paper we bring query expansion into the visual domain via two novel contributions. Firstly, strong spatial constraints between the query image and each result allow us to accurately verify each return, suppressing the false positives which typically ruin text-based query expansion. Secondly, the verified images can be used to learn a latent feature model to enable the controlled construction of expanded queries. We illustrate these ideas on the 5000 annotated image Oxford building database together with more than 1M Flickr images. We show that the precision is substantially boosted, achieving total recall in many cases.

title: Video Google: a text retrieval approach to object matching in videos
abstract: We describe an approach to object and scene retrieval which searches for and localizes all the occurrences of a user outlined object in a video. The object is represented by a set of viewpoint invariant region descriptors so that recognition can proceed successfully despite changes in viewpoint, illumination and partial occlusion. The temporal continuity of the video within a shot is used to track the regions in order to reject unstable regions and reduce the effects of noise in the descriptors. The analogy with text retrieval is in the implementation where matches on descriptors are pre-computed (using vector quantization), and inverted file systems and document rankings are used. The result is that retrieved is immediate, returning a ranked list of key frames/shots in the manner of Google. The method is illustrated for matching in two full length feature films.

title: SURF: Speeded Up Robust Features
abstract: In this paper, we present a novel scale- and rotation-invariant interest point detector and descriptor, coined SURF (Speeded Up Robust Features). It approximates or even outperforms previously proposed schemes with respect to repeatability, distinctiveness, and robustness, yet can be computed and compared much faster. 
 
This is achieved by relying on integral images for image convolutions; by building on the strengths of the leading existing detectors and descriptors (in casu, using a Hessian matrix-based measure for the detector, and a distribution-based descriptor); and by simplifying these methods to the essential. This leads to a combination of novel detection, description, and matching steps. The paper presents experimental results on a standard evaluation set, as well as on imagery obtained in the context of a real-life object recognition application. Both show SURF's strong performance.

title: Efficient representation of local geometry for large scale object retrieval
abstract: State of the art methods for image and object retrieval exploit both appearance (via visual words) and local geometry (spatial extent, relative pose). In large scale problems, memory becomes a limiting factor - local geometry is stored for each feature detected in each image and requires storage larger than the inverted file and term frequency and inverted document frequency weights together. We propose a novel method for learning discretized local geometry representation based on minimization of average reprojection error in the space of ellipses. The representation requires only 24 bits per feature without drop in performance. Additionally, we show that if the gravity vector assumption is used consistently from the feature description to spatial verification, it improves retrieval performance and decreases the memory footprint. The proposed method outperforms state of the art retrieval algorithms in a standard image retrieval benchmark.

title: Retrieving landmark and non-landmark images from community photo collections
abstract: State of the art data mining and image retrieval in community photo collections typically focus on popular subsets, e.g. images containing landmarks or associated to Wikipedia articles. We propose an image clustering scheme that, seen as vector quantization compresses a large corpus of images by grouping visually consistent ones while providing a guaranteed distortion bound. This allows us, for instance, to represent the visual content of all thousands of images depicting the Parthenon in just a few dozens of scene maps and still be able to retrieve any single, isolated, non-landmark image like a house or graffiti on a wall. Starting from a geo-tagged dataset, we first group images geographically and then visually, where each visual cluster is assumed to depict different views of the the same scene. We align all views to one reference image and construct a 2D scene map by preserving details from all images while discarding repeating visual features. Our indexing, retrieval and spatial matching scheme then operates directly on scene maps. We evaluate the precision of the proposed method on a challenging one-million urban image dataset.

title: Bundling features for large scale partial-duplicate web image search
abstract: In state-of-the-art image retrieval systems, an image is represented by a bag of visual words obtained by quantizing high-dimensional local image descriptors, and scalable schemes inspired by text retrieval are then applied for large scale image indexing and retrieval. Bag-of-words representations, however: 1) reduce the discriminative power of image features due to feature quantization; and 2) ignore geometric relationships among visual words. Exploiting such geometric constraints, by estimating a 2D affine transformation between a query image and each candidate image, has been shown to greatly improve retrieval precision but at high computational cost. In this paper we present a novel scheme where image features are bundled into local groups. Each group of bundled features becomes much more discriminative than a single feature, and within each group simple and robust geometric constraints can be efficiently enforced. Experiments in Web image search, with a database of more than one million images, show that our scheme achieves a 49% improvement in average precision over the baseline bag-of-words approach. Retrieval performance is comparable to existing full geometric verification approaches while being much less computationally expensive. When combined with full geometric verification we achieve a 77% precision improvement over the baseline bag-of-words approach, and a 24% improvement over full geometric verification alone.

title: Feature map hashing: sub-linear indexing of appearance and global geometry
abstract: We present a new approach to image indexing and retrieval, which integrates appearance with global image geometry in the indexing process, while enjoying robustness against viewpoint change, photometric variations, occlusion, and background clutter. We exploit shape parameters of local features to estimate image alignment via a single correspondence. Then, for each feature, we construct a sparse spatial map of all remaining features, encoding their normalized position and appearance, typically vector quantized to visual word. An image is represented by a collection of such feature maps and RANSAC-like matching is reduced to a number of set intersections. Because the induced dissimilarity is still not a metric, we extend min-wise independent permutations to collections of sets and derive a similarity measure for feature map collections. We then exploit sparseness to build an inverted file whereby the retrieval process is sub-linear in the total number of images, ideally linear in the number of relevant ones. We achieve excellent performance on 10^4 images, with a query time in the order of milliseconds.