Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search

Hervé JégouMatthijs DouzeCordelia Schmid

article2008ECCV2,102 citations

Presents Hamming embedding and weak geometric consistency to refine visual-word descriptor matching and filter geometrically inconsistent features directly within an inverted file, substantially increasing retrieval accuracy on million-scale image databases.

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Large-scale image retrieval systems face significant challenges when searching through millions of images. Standard industry approaches rely on the "bag-of-features" method, which quantizes local image features into discrete visual words and indexes them using inverted files. While fast and memory-efficient, this quantization discards critical descriptor precision and ignores geometric spatial relationships, leading to high rates of false visual matches and degraded search accuracy as databases scale.

The article demonstrates that augmenting visual words with compact binary signatures and filtering matches through weak geometric constraints dramatically improves retrieval accuracy without sacrificing runtime efficiency or requiring excessive memory.

To evaluate this, the authors developed and tested two complementary mechanisms directly embedded within an inverted file index: Hamming Embedding, which assigns a 64-bit binary signature to refine matches within visual clusters, and Weak Geometric Consistency, which checks for consistency in angle and scale differences between matching points. The framework was evaluated on benchmark datasets including the INRIA Holidays dataset, Oxford Buildings, and a large distractor collection of one million Flickr images.

The findings show that combining Hamming Embedding and Weak Geometric Consistency roughly doubles search precision compared to baseline methods. On the one-million-image dataset, the combined approach identified 61.8% of correct results in the top 100 images, compared to only 30.6% for the standard bag-of-features baseline. Furthermore, Hamming Embedding accelerated query times because rapid bitwise filtering reduced downstream score updates, resulting in total query times comparable to or faster than traditional indexes while maintaining a compact memory footprint of only 12 bytes per feature.

These results demonstrate that organizations managing large visual repositories can achieve state-of-the-art search precision at web scale while avoiding the massive computational overhead of full spatial verification. Weak geometric filtering effectively purifies candidate shortlists across millions of images, making optional secondary re-ranking stages substantially more effective.

Organizations should adopt 64-bit Hamming Embedding combined with weak geometric checks as a standard indexing architecture for million-scale image search pipelines. However, decision-makers should note that optimal performance relies on representative offline training data to establish quantization medians, and Weak Geometric Consistency requires structured orientation priors to achieve maximum accuracy across varied photography styles.

INRIA descriptors geometric transformations hamming distance Hamming embedding weak geometric consistency large scale image search

Jégou et al (2008).pdf

Paper: Distinctive Image Features from Scale-Invariant Keypoints, David G. Lowe (2004). Read this foundation in SIFT keypoints and descriptors first: the source relies on local-feature matching and visual-word indexing to introduce its precision-preserving refinements.
Paper: Visual categorization with bags of keypoints, Gabriella Csurka et al. (2004). Its bag-of-keypoints pipeline establishes the visual-word quantization baseline that the source augments with binary signatures and geometric filtering.
Paper: Local Grayvalue Invariants for Image Retrieval, Cordelia Schmid et al. (1997). Its local invariant features and semilocal geometric checks provide an earlier basis for understanding the source’s local matching and weak consistency tests.

Paper: Aggregating Local Image Descriptors into Compact Codes, Hervé Jégou et al. (2012). After the source’s compact binary filtering within an inverted index, this work advances large-scale image retrieval with aggregated descriptors and product-quantized codes.
Paper: Global-to-Local or Local-to-Global? Enhancing Image Retrieval with Efficient Local Search and Effective Global Re-ranking, Dror Aiger et al. (2025). Building on local-feature retrieval, this later system reverses the usual search order and combines scalable local matching with global re-ranking.

Cover for Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search

Abstract

This paper improves recent methods for large scale image search. State-of-the-art methods build on the bag-of-features image representation. We, first, analyze bag-of-features in the framework of approximate nearest neighbor search. This shows the sub-optimality of such a representation for matching descriptors and leads us to derive a more precise representation based on 1) Hamming embedding (HE) and 2) weak geometric consistency constraints (WGC). HE provides binary signatures that refine the matching based on visual words. WGC filters matching descriptors that are not consistent in terms of angle and scale. HE and WGC are integrated within the inverted file and are efficiently exploited for all images, even in the case of very large datasets. Experiments performed on a dataset of one million of images show a significant improvement due to the binary signature and the weak geometric consistency constraints, as well as their efficiency. Estimation of the full geometric transformation, i.e., a re-ranking step on a short list of images, is complementary to our weak geometric consistency constraints and allows to further improve the accuracy.

Topics

descriptors geometric transformations hamming distance image representations image search nearest neighbor search

Keywords

Hamming embedding weak geometric consistency large scale image search approximate nearest neighbor search object retrieval visual vocabulary local descriptors binary signatures Hamming distance

1 Introduction
2 Voting Interpretation of Bag-of-Features
2.1 Voting Approach
2.2 Bag-of-Features: Voting and Approximate NN Interpretation
2.3 Weakness of Quantization-Based Approaches
3 Hamming Embedding of Local Image Descriptors
4 Large-Scale Geometric Consistency
4.1 Weak Geometrical Consistency
4.2 Injecting a Priori Knowledge
5 Complexity
6 Experiments
6.1 Datasets
6.2 Evaluation of HE and WGC
7 Conclusion
References

Knowls

Knowl 1 — Offline Learning and Binary Signature Extraction for Hamming Embedding
algorithm
Hamming Embedding (HE) refines visual word quantization by associating each local descriptor with a compact binary signature that encodes its position within its assigned Voronoi cell. The procedure consists of an offline learning phase and an online signature extraction phase.
Offline Learning:
Input: Training set of local descriptors $X = \{x_1, \dots, x_N\} \subset \mathbb{R}^d$ , number of visual words $k$ , visual word quantizer $q: \mathbb{R}^d \to \{1, \dots, k\}$ , signature length $d_b$ .
Output: Projection matrix $P \in \mathbb{R}^{d_b \times d}$ , median thresholds $\tau_{l,h}$ for $l \in \{1, \dots, k\}$ and $h \in \{1, \dots, d_b\}$ .
1. Generate a random matrix $G \in \mathbb{R}^{d \times d_b}$ with independent standard Gaussian entries.
2. Compute the QR decomposition of $G$ , and set $P$ to the transpose of the orthogonal component, yielding a $d_b \times d$ orthogonal projection matrix.
3. For each training descriptor $x_i \in X$ :
    a. Assign $x_i$ to its visual word centroid $l = q(x_i)$ .
    b. Compute the projection $z_i = P x_i = (z_{i1}, \dots, z_{i d_b})^\top \in \mathbb{R}^{d_b}$ .
4. For each visual word $l \in \{1, \dots, k\}$ and component $h \in \{1, \dots, d_b\}$ :
    a. Compute $\tau_{l,h} = \text{median}(\{z_{ih} \mid q(x_i) = l\})$ .
return $P, \{\tau_{l,h}\}$
Online Signature Extraction:
Input: Local descriptor $x \in \mathbb{R}^d$ , quantizer $q$ , projection matrix $P$ , thresholds $\tau_{l,h}$ .
Output: Quantized visual word index $q(x) \in \{1, \dots, k\}$ , binary signature $b(x) = (b_1(x), \dots, b_{d_b}(x)) \in \{0, 1\}^{d_b}$ .
1. Assign $x$ to its closest centroid $q(x) = \arg\min_l \|x - c_l\|_2$ .
2. Compute the projected vector $z = P x = (z_1, \dots, z_{d_b})^\top$ .
3. For $h = 1$ to $d_b$ :
    if $z_h > \tau_{q(x), h}$ :
         $b_h(x) \leftarrow 1$
    else:
         $b_h(x) \leftarrow 0$
return $q(x), b(x)$
For standard 128-dimensional SIFT descriptors ( $d=128$ ), setting $d_b = 64$ bits provides an effective trade-off between descriptor filtering quality and memory overhead (8 bytes per descriptor).
Knowl 2 — Hamming Embedding Descriptor Matching Function
equation
In Hamming Embedding (HE), two local descriptors $x, y \in \mathbb{R}^d$ are matched only if they are assigned to the same visual word $q(x) = q(y) \in \{1, \dots, k\}$ and their binary signatures $b(x), b(y) \in \{0, 1\}^{d_b}$ have a Hamming distance $h(b(x), b(y))$ below or equal to a predefined threshold $h_t \in {0, \dots, d_b}.

The Hamming distance between binary signatures is defined as:

$h(b(x), b(y)) = \sum_{i=1}^{d_b} [b_i(x) \neq b_i(y)]$

where $[\cdot]$ is the Iverson bracket ( $1$ if true, $0$ if false), computed via the bitwise XOR and popcount operations.

The HE matching score between descriptors $x$ and $y$ is given by:

$f_{\text{HE}}(x, y) = \begin{cases} \text{tf-idf}(q(x)) & \text{if } q(x) = q(y) \text{ and } h(b(x), b(y)) \le h_t, \\ 0 & \text{otherwise,} \end{cases}$

where $\text{tf-idf}(l)$ denotes the term frequency-inverse document frequency weighting of visual word $l$ .

By setting $h_t$ appropriately (typically $h_t \in [20, 26]$ for $d_b = 64$ ), the matching function filters out the majority of false-positive descriptors that fall into the same Voronoi cell while preserving genuine Euclidean nearest neighbors.
Knowl 3 — Weak Geometric Consistency (WGC) Scoring via Decoupled Histograms
model/method
Weak Geometric Consistency (WGC) filters visual word matches between a query image and a database image $j$ by checking the consistency of orientation and scale differences between the corresponding local interest regions.

For each matching pair of descriptors $(x_{i,j}, y_{i'})$ , let $\delta_a \in [-\pi, \pi)$ denote their quantized angle difference and $\delta_s \in \mathbb{R}$ their quantized log-scale difference ( $\delta_s = \log s(x_{i,j}) - \log s(y_{i'})$ ). Because full 2D transformation estimation is computationally expensive for large-scale datasets, WGC maintains two decoupled 1D accumulation histograms per database image $j$ : an angle difference histogram $s_j^a(\delta_a)$ and a log-scale difference histogram $s_j^s(\delta_s)$ .

When processing matched descriptor pairs $(x_{i,j}, y_{i'})$ , both histograms are independently updated:

$s_j^a(\delta_a) := s_j^a(\delta_a) + f(x_{i,j}, y_{i'})$

$s_j^s(\delta_s) := s_j^s(\delta_s) + f(x_{i,j}, y_{i'})$

where $f(x_{i,j}, y_{i'})$ is the descriptor matching weight (e.g., $f_{\text{HE}}(x_{i,j}, y_{i'})$ ).

The histograms are smoothed with a moving average filter to reduce bin-boundary quantization artifacts. The aggregate image similarity score $s_j^*$ is then computed as the minimum of the two maximum marginal scores:

$s_j^* = g\left(\min\left(\max_{\delta_a} s_j^a(\delta_a), \; \max_{\delta_s} s_j^s(\delta_s)\right)\right)$

where $g(\cdot)$ applies score normalization (such as $L_2$ norm division by the square root of the number of descriptors). This decoupled formulation approximates the maximum bin of a full 2D angle-scale histogram while maintaining low memory overhead and fast execution during inverted file traversal.
Knowl 4 — A Priori Knowledge Weighting in Weak Geometric Consistency
model/method
Weak Geometric Consistency can be enhanced by incorporating empirical prior distributions over angle differences $\delta_a$ and log-scale differences $\delta_s$ between matching images.

In real-world image datasets, matched features exhibit non-uniform geometric transformation distributions:
1. Scale Prior: Matching image pairs frequently share similar scales, producing a sharp mode at $\delta_s = 0$ (log-scale difference of zero).
2. Orientation Priors:
  - Same Orientation Prior: For datasets where images are captured upright (such as architectural datasets like Oxford5k), the angle difference distribution is heavily concentrated around $\delta_a = 0$ .
  - $\pi/2$ Rotation Prior: For general consumer photo collections (such as personal holiday photos), cameras are primarily oriented in portrait or landscape orientations, leading to sharp peaks at $\delta_a \in \{0, \pi/2, \pi, 3\pi/2\}$ .
Before extracting the maximum histogram bins $\max_{\delta_a} s_j^a(\delta_a)$ and $\max_{\delta_s} s_j^s(\delta_s)$ , the histogram bin values are multiplied by corresponding empirical prior weights. This downweights votes corresponding to unnatural rotations or extreme scale changes, reducing false-positive matches.
Knowl 5 — Inverted File Layout and Computational Optimizations for HE and WGC
model/method
To support Hamming Embedding (HE) and Weak Geometric Consistency (WGC) at scale, the standard bag-of-features inverted file is modified to store descriptor-level entries rather than image-level counts.

Each entry in an inverted list corresponds to a single descriptor and requires 12 bytes (96 bits) of storage:
- Image ID: 21 bits (sufficient to address up to 2 million database images).
- Orientation: 6 bits (quantizing region orientation into 64 discrete angle bins).
- Log-Scale: 5 bits (quantizing region scale into 32 discrete scale bins).
- Binary Signature: 64 bits (the $d_b = 64$ Hamming embedding signature).
During query execution:
1. Hamming Distance Filtering: For each inverted list entry associated with a query descriptor's visual word, the Hamming distance between the 64-bit query signature and database entry signature is evaluated using bitwise XOR and popcount. Entries with Hamming distance $> h_t$ are immediately discarded without updating image accumulators. Because this early rejection prunes a high percentage of candidate matches, HE actually reduces total inverted index query time compared to the baseline bag-of-features index.
2. WGC Histogram Accumulation: For surviving entries, the difference in orientation (6-bit difference) and scale (5-bit difference) index into small per-image accumulators (requiring 128 floating-point values per active image), which are subsequently smoothed and evaluated for their peak marginal values.
Knowl 6 — INRIA Holidays Dataset and Evaluation Protocol
experimental setup
The INRIA Holidays dataset is a benchmark designed to evaluate particular object and scene retrieval under diverse transformations.

Dataset Composition:
- Total Images: 1491 high-resolution personal holiday photographs representing a wide variety of scene types (natural landscapes, man-made architecture, fire/water effects).
- Queries and Groups: 500 distinct scene/object groups. Each group contains one designated query image (500 total queries) and one or more ground-truth matching images representing the same scene or object under varying rotations, viewpoints, illumination changes, and blur.
- Descriptors: Local features extracted using the Hessian-Affine interest point detector and 128-dimensional SIFT descriptors (approximately 4.456 million descriptors across the 1491 images).
Distractor and Vocabulary Sets:
- Flickr60k: 67,714 images (140 million descriptors) used strictly as an independent training dataset to learn $k$ -means visual word centroids (with vocabulary sizes $k = 20{,}000$ and $k = 200{,}000$ ) and HE median projection thresholds $\tau_{l,h}$ .
- Flickr1M: 1 million distractor images (2.072 billion descriptors) added to Holidays to evaluate search performance at scale.
Evaluation Metric: Mean Average Precision (mAP) computed over all 500 query precision-recall curves.

Knowl 7 — Retrieval Performance of HE, WGC, and Combined Methods on Holidays and Oxford5k

data/table

Retrieval performance was evaluated on the Holidays dataset (500 queries) and Oxford5k dataset (55 queries) using an independent visual vocabulary trained on Flickr60k for vocabulary sizes $k = 20{,}000$ and $k = 200{,}000$ .

Parameters			Holidays		Oxford5k
Method	HE: $h_t$	WGC	$k = 20000$	$k = 200000$	$k = 20000$	$k = 200000$
baseline BOF	-	-	0.4463	0.5488	0.3854	0.3950
HE	20	-	0.7268	0.7093	0.4798	0.4503
HE	22	-	0.7181	0.7074	0.4892	0.4571
HE	24	-	0.6947	0.7115	0.4906	0.4585
HE	26	-	0.6649	0.6879	0.4794	0.4624
WGC	-	no prior	0.5996	0.6116	0.3749	0.3833
WGC	-	with prior	0.6446	0.6859	0.4375	0.4602
HE+WGC	20	with prior	0.7391	0.7328	0.5442	0.5096
HE+WGC	22	with prior	0.7463	0.7382	0.5472	0.5217
HE+WGC	24	with prior	0.7507	0.7439	0.5397	0.5252
HE+WGC	26	with prior	0.7383	0.7404	0.5253	0.5275

The data shows:

Hamming Embedding (HE) substantially outperforms baseline Bag-of-Features (BOF), boosting mAP on Holidays from 0.4463 to 0.7268 ( $k=20000$ ) and on Oxford5k from 0.3854 to 0.4906.
Weak Geometric Consistency (WGC) alone provides noticeable gains, especially when combined with orientation priors (raising Holidays mAP to 0.6859 at $k=200000$ ).
Combining HE and WGC yields the best results across all settings, reaching 0.7507 mAP on Holidays and 0.5472 mAP on Oxford5k.
When using an independent visual vocabulary, smaller vocabularies ( $k=20{,}000$ ) with HE match or surpass larger vocabularies ( $k=200{,}000$ ), because HE signature matching compensates for coarse visual word partitioning.

Knowl 8 — Memory Usage and Query Latency Across Indexing Configurations on 1 Million Images

data/table

Descriptor memory usage in the inverted file and average query times were measured on a 2.6 GHz quad-core processor for the 1 million image dataset (Flickr1M distractors combined with Holidays).

Descriptor Memory Usage		Time per Query Image (Flickr1M Dataset)
Field	Size	Stage / Method	$k = 20000$	$k = 200000$
Image ID	21 bits	Compute descriptors	0.88 s	0.88 s
Orientation	6 bits	Quantization + binary signature	0.36 s	0.60 s
Log-scale	5 bits	Search, baseline BOF	2.74 s	0.62 s
Binary signature	64 bits	Search, WGC	10.19 s	2.11 s
Total WGC	4 bytes	Search, HE	1.16 s	0.20 s
Total HE	12 bytes	Search, HE+WGC	1.82 s	0.65 s
Total WGC+HE	12 bytes

Key observations:

Memory Footprint: Storing descriptor metadata for combined WGC and HE requires 12 bytes per indexed descriptor (96 bits), enabling memory alignment.
Search Speed: Standalone HE search is faster than baseline BOF search (1.16 s vs. 2.74 s for $k=20000$ ; 0.20 s vs. 0.62 s for $k=200000$ ) because XOR thresholding rapidly discards candidate list entries and avoids accumulator updates.
Combined Search Efficiency: HE+WGC search latency (1.82 s for $k=20000$ and 0.65 s for $k=200000$ ) is lower than or comparable to baseline inverted file search while significantly outperforming it in retrieval precision.

Knowl 9 — Large-Scale Search Robustness and Complementarity with Full Geometric Re-Ranking
empirical result
When scaling the database from 991 to 1,000,991 images by adding distractors from Flickr1M to the INRIA Holidays dataset ( $k=200{,}000$ ), Hamming Embedding combined with Weak Geometric Consistency (HE+WGC) demonstrates superior robustness to distractors compared to standard Bag-of-Features (BOF).

True Positive Recall in Top-100 Shortlist ( $k=200{,}000$ ):
- At 991 images: BOF achieves a true positive rate of 0.673, whereas HE+WGC achieves 0.855.
- At 10,991 images: BOF achieves 0.557, whereas HE+WGC achieves 0.789.
- At 100,991 images: BOF achieves 0.431, whereas HE+WGC achieves 0.708.
- At 1,000,991 images: BOF retains only 0.306 of true positives in the top 100, whereas HE+WGC retains 0.618 (more than double the baseline rate).
Complementarity with Full Geometric Re-Ranking: Applying full 2D affine transformation estimation (spatial verification via a 4-DOF Hough transform followed by affine fitting) on the top-100 shortlist returned by HE+WGC further improves retrieval mAP across all database sizes. For example, on 1 million images, re-ranking the HE+WGC shortlist increases mAP from approximately 0.55 to nearly 0.70, confirming that weak geometric constraints applied across the entire database and full spatial verification applied to a candidate shortlist are complementary.

Coverage note — None was omitted; all key contributions—Hamming embedding, weak geometric consistency, inverted file index structure, benchmarks, and 1M image scaling experiments—are covered.

References

1.Lowe, D.: Distinctive image features from scale-invariant keypoints. IJCV 60, 91– 110 (2004)
2.Mikolajczyk, K., Schmid, C.: Scale and affine invariant interest point detectors. IJCV 60(1), 63–86 (2004)
3.Matas, J., Chum, O., Martin, U., Pajdla, T.: Robust wide baseline stereo from maximally stable extremal regions. In: BMVC, pp. 384–393 (2002)
4.Sivic, J., Zisserman, A.: Video Google: A text retrieval approach to object matching in videos. In: ICCV, pp. 1470–1477 (2003)
5.Nist´er, D., Stew´enius, H.: Scalable recognition with a vocabulary tree. In: CVPR, pp. 2161–2168 (2006)
6.Omercevic, D., Drbohlav, O., Leonardis, A.: High-dimensional feature matching: employing the concept of meaningful nearest neighbors. In: ICCV (2007)
7.Datar, M., Immorlica, N., Indyk, P., Mirrokni, V.: Locality-sensitive hashing scheme based on p-stable distributions, pp. 253–262 (2004)
8.Shakhnarovich, G., Darrell, T., Indyk, P.: Nearest-Neighbor Methods in Learning and Vision: Theory and Practice. MIT Press, Cambridge (2006)
9.Philbin, J., Chum, O., Isard, M.A., Zisserman, J.S.: Object retrieval with large vocabularies and fast spatial matching. In: CVPR (2007)
10.Jegou, H., Harzallah, H., Schmid, C.: A contextual dissimilarity measure for accu- rate and efficient image search. In: CVPR (2007)
11.Fraundorfer, F., Stewenius, H., Nister, D.: A binning scheme for fast hard drive based image search. In: CVPR (2007)
12.Schindler, G., Brown, M., Szeliski, R.: City-scale location recognition. In: CVPR (2007)
13.Philbin, J., Chum, O., Isard, M., Sivic, J., Zisserman, A.: Lost in quantization: Improving particular object retrieval in large scale image databases. In: CVPR (2008)
14.Jegou, H., Douze, M.: INRIA Holidays dataset (2008), http://lear.inrialpes.fr/people/jegou/data.php
15.Mikolajczyk, K.: Binaries for affine covariant region descriptors (2007), http://www.robots.ox.ac.uk/∼vgg/research/affine/

Citation

MLA

Jegou, H., et al. “Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search”. Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2008, pp. 304–17, https://doi.org/10.1007/978-3-540-88682-2_24.

APA

Jegou, H., Douze, M., & Schmid, C. (2008). Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search. In Lecture Notes in Computer Science (pp. 304–317). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-88682-2_24

Chicago

Jegou, H., M. Douze, and C. Schmid. 2008. “Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search”. In Lecture Notes in Computer Science. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-88682-2_24.

Harvard

Jegou, H., Douze, M. and Schmid, C. (2008) “Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search”, Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp. 304–317. Available at: https://doi.org/10.1007/978-3-540-88682-2_24.

Vancouver

1. Jegou H, Douze M, Schmid C (2008) Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search. In: Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp 304–317

BibTeX

@inbook{Jegou_2008, title={Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search}, ISBN={9783540886822}, ISSN={1611-3349}, url={http://dx.doi.org/10.1007/978-3-540-88682-2_24}, DOI={10.1007/978-3-540-88682-2_24}, booktitle={Computer Vision – ECCV 2008}, publisher={Springer Berlin Heidelberg}, author={Jegou, Herve and Douze, Matthijs and Schmid, Cordelia}, year={2008}, pages={304–317} }

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Hamming Embedding and Weak Geometric Consistency for Large Scale Image Search

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Offline Learning and Binary Signature Extraction for Hamming Embedding

Knowl 2 — Hamming Embedding Descriptor Matching Function

Knowl 3 — Weak Geometric Consistency (WGC) Scoring via Decoupled Histograms

Knowl 4 — A Priori Knowledge Weighting in Weak Geometric Consistency

Knowl 5 — Inverted File Layout and Computational Optimizations for HE and WGC

Knowl 6 — INRIA Holidays Dataset and Evaluation Protocol