A Comparison of Affine Region Detectors

K. MikolajczykT. TuytelaarsCordelia SchmidAndrew ZissermanJiri MatasF. SchaffalitzkyT. KadirL. Gool

article2005IJCV3,522 citations

Establishes the standard benchmark dataset and quantitative evaluation protocol for assessing affine covariant region detectors across diverse imaging transformations, providing systematic performance comparisons of leading methods like MSER, Harris-Affine, and Hessian-Affine.

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This paper evaluates and compares six affine covariant region detectors developed for robust local feature matching in computer vision applications such as wide-baseline stereo, object recognition, image retrieval, and robot localization. These detectors identify image regions whose shape adapts automatically to viewpoint and illumination changes so that the same physical surface patch can be described consistently across images. The work addresses the lack of standardized performance data by testing the detectors on a shared benchmark of planar scenes under controlled transformations.

The study set out to measure how well each detector finds repeatable and distinctive regions across changes in viewpoint, scale, blur, compression, and illumination, while also establishing public test images and evaluation code for future comparisons.

The authors implemented the detectors using code supplied by their creators and ran them on eight image sequences containing both structured scenes with distinct edges and textured scenes with repeated patterns. Repeatability was quantified by projecting detected elliptical regions through known homographies and measuring normalized overlap error. Distinctiveness was assessed by attaching 128-dimensional SIFT descriptors to the regions and counting correct nearest-neighbor matches.

MSER and Hessian-Affine detectors achieved the highest repeatability scores on most sequences, often exceeding 60 percent for moderate viewpoint or scale changes and remaining above 40 percent for larger deformations; Harris-Affine followed closely, while edge-based, intensity-extrema, and salient-region detectors performed well only on particular scene types. Absolute numbers of repeatable regions also varied widely, with Hessian-Affine and Harris-Affine typically returning several times more correspondences than the others. Matching scores using SIFT descriptors tracked the repeatability results for most transformations, indicating that the regions are sufficiently distinctive for automatic correspondence, although performance degraded noticeably on highly repetitive textures or under strong blur.

These results matter because practitioners can now select or combine detectors according to scene characteristics and application constraints rather than relying on anecdotal evidence. The public benchmark further enables objective progress tracking as new detectors appear.

The authors recommend running several complementary detectors in parallel to increase coverage and robustness, then filtering matches with geometric consistency checks. They also note that future detectors should be evaluated on the same data and protocol.

The evaluation is restricted to planar scenes or fixed-camera sequences related by homographies, uses default parameter settings, and measures performance only on the supplied medium-resolution images; results on non-planar 3D scenes or very different image statistics may differ. Overall confidence in the reported ordering of detectors on the tested conditions is high because the protocol is transparent, the data are public, and multiple performance metrics were examined.

Czech Technical University in Prague INRIA KU Leuven University of Oxford detection algorithm high resolution image detector arrays Affine Region Detector Harris-Affine Hessian-Affine

Mikolajczyk et al (2005).pdf

Paper: A performance evaluation of local descriptors, Krystian Mikolajczyk et al. (2005). Reading this evaluation of local descriptors first provides the necessary background on how feature representations are paired with the affine region detectors evaluated in the source paper.

Paper: SURF: Speeded Up Robust Features, Herbert Bay et al. (2006). This paper builds directly upon the foundational affine and scale-invariant detectors benchmarked in the source by introducing faster approximate detector-descriptor designs.
Paper: BRIEF: Binary Robust Independent Elementary Features, Michael Calonder et al. (2010). This paper extends the local feature paradigm established by the source and its contemporaries into ultra-fast binary descriptors suitable for resource-constrained platforms.

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Abstract

The paper gives a snapshot of the state of the art in affine covariant region detectors, and compares their performance on a set of test images under varying imaging conditions. Six types of detectors are included: detectors based on affine normalization around Harris (Mikolajczyk and Schmid, 2002; Schaffalitzky and Zisserman, 2002) and Hessian points (Mikolajczyk and Schmid, 2002), a detector of ‘maximally stable extremal regions’, proposed by Matas et al. (2002); an edge-based region detector (Tuytelaars and Van Gool, 1999) and a detector based on intensity extrema (Tuytelaars and Van Gool, 2000), and a detector of ‘salient regions’,

Topics

detection algorithm high resolution image detector arrays

Keywords

Affine Region Detector Harris-Affine Hessian-Affine MSER Edge-Based Region Intensity Extrema Salient Region Repeatability Homography SIFT Descriptor

A Comparison of Affine Region Detectors
1. Introduction
2. Affine Covariant Detectors
2.1. Detectors Based on Affine Normalization—Harris-Affine & Hessian-Affine
2.2. An Edge-Based Region Detector
2.3. Intensity Extrema-Based Region Detector
2.4. Maximally Stable Extremal Region Detector
2.5. Salient Region Detector
3. The Image Data Set
3.1. Discussion
4. Overlap Comparison Using Homographies
4.1. Repeatability Measure
4.2. Repeatability Under Various Transformations
4.3. More Detailed Tests
5. Matching Experiments
5.1. Matching Score
6. Conclusions

Knowls

Knowl 1 — Overlap Error and Repeatability Evaluation Metric for Affine Region Detectors
definition
To quantitatively evaluate affine covariant region detectors independently of specific descriptor matching algorithms, detector accuracy is defined through the geometric overlap of detected regions under a ground truth planar homography.

An elliptical affine region in an image is defined as: $R_\mu = \{ \mathbf{x} \in \mathbb{R}^2 \mid \mathbf{x}^T \mu \mathbf{x} \le 1 \}$ where $\mu$ is a $2 \times 2$ symmetric positive-definite matrix representing the shape and size of the ellipse. Given a ground truth homography $H$ that maps coordinates from the reference image $A$ to target image $B$ , an ellipse $\mu_b$ detected in image $B$ projects onto image $A$ as $H^T \mu_b H$ .

The overlap error $\epsilon_O$ between an ellipse $R_{\mu_a}$ detected in image $A$ and an ellipse $R_{\mu_b}$ detected in image $B$ (projected onto $A$ ) is: $\epsilon_O = 1 - \frac{\text{Area}(R_{\mu_a} \cap R_{H^T \mu_b H})}{\text{Area}(R_{\mu_a} \cup R_{H^T \mu_b H})}$

Two regions are deemed to correspond if their overlap error is below a predefined threshold, $\epsilon_O < \epsilon_0$ (typically $\epsilon_0 = 0.40$ , which corresponds to an approximate $20\%$ difference in region radii).

To prevent detectors with intrinsically larger regions from receiving artificially higher overlap scores due to spatial scaling effects, both the reference ellipse $R_{\mu_a}$ and the mapped ellipse $R_{H^T \mu_b H}$ are normalized by a uniform scaling factor $s$ such that the reference ellipse has an equivalent circular radius of $r_0 = 30$ pixels prior to numerical calculation of area union and intersection.

The repeatability score for an image pair is defined as the ratio of valid correspondences to the maximum possible number of correspondences in the shared field of view: $\text{Repeatability} = \frac{N_{\text{corr}}}{\min(N_a, N_b)}$ where $N_{\text{corr}}$ is the number of mutually corresponding region pairs, and $N_a, N_b$ are the counts of regions detected in the shared visible scene area of images $A$ and $B$ , respectively.
Knowl 2 — SIFT-Based Matching Score Metric for Affine Covariant Regions
experimental setup
To evaluate the distinctiveness and matching capability of detected affine regions, local appearance within each region is normalized and encoded using the 128-dimensional Scale-Invariant Feature Transform (SIFT) descriptor.
1. Affine Geometric and Photometric Normalization: Each detected elliptical region $R_\mu$ is mapped to a canonical circular patch of $30 \times 30$ pixels using the matrix transformation $\mu^{1/2}$ . To capture surrounding contextual texture, the measurement region is scaled by a factor of 3 relative to the detected distinguished region size. The patch is then rotated to align with the dominant gradient orientation, achieving invariance to 2D affine deformations and rotations.
2. Ground Truth Correspondence: A detected region pair $(R_{\mu_a}, R_{\mu_b})$ is labeled as a ground truth match if its normalized overlap error under the known inter-image homography $H$ satisfies $\epsilon_O \le 0.40$ . Each region in image $A$ is restricted to at most one ground truth match.
3. Descriptor Matching: Descriptors computed for regions in the target image are matched to their nearest neighbor in the reference image using Euclidean distance in the 128-dimensional SIFT space.
4. Matching Score Definition: The matching score measures the proportion of detected regions that form geometrically correct nearest-neighbor matches: $\text{Matching Score} = \frac{N_{\text{correct}}}{\min(N_a, N_b)}$ where $N_{\text{correct}}$ is the number of nearest-neighbor descriptor matches that satisfy $\epsilon_O \le 0.40$ , and $N_a, N_b$ are the number of detected regions lying in the common scene area.
Knowl 3 — Harris-Affine and Hessian-Affine Detectors
model/method
The Harris-Affine and Hessian-Affine detectors identify multi-scale interest points and iteratively adapt their local elliptical shape to achieve affine covariance.
1. Multi-Scale Point Detection:
  - Harris-Affine locates spatial extrema of the cornerness measure derived from the second moment matrix (auto-correlation matrix): $M(\mathbf{x}, \sigma_I, \sigma_D) = \sigma_D^2 \, g(\sigma_I) * \begin{bmatrix} I_x^2(\mathbf{x}, \sigma_D) & I_x I_y(\mathbf{x}, \sigma_D) \\ I_x I_y(\mathbf{x}, \sigma_D) & I_y^2(\mathbf{x}, \sigma_D) \end{bmatrix}$ where $\sigma_D$ is the differentiation scale, $\sigma_I$ is the integration scale, and $g(\sigma)$ is a Gaussian smoothing filter.
  - Hessian-Affine locates spatial extrema of the determinant of the Hessian matrix: $H(\mathbf{x}, \sigma_D) = \begin{bmatrix} I_{xx}(\mathbf{x}, \sigma_D) & I_{xy}(\mathbf{x}, \sigma_D) \\ I_{xy}(\mathbf{x}, \sigma_D) & I_{yy}(\mathbf{x}, \sigma_D) \end{bmatrix}$ penalizing elongated ridge structures and selecting blob-like features.
2. Characteristic Scale Selection: For each spatial point $\mathbf{x}$ , the characteristic scale $\sigma_D$ is chosen where the scale-normalized Laplacian $\sigma_D^2 |I_{xx}(\mathbf{x}, \sigma_D) + I_{yy}(\mathbf{x}, \sigma_D)|$ attains a local extremum over continuous scale space.
3. Iterative Affine Shape Adaptation: Given an initial point and scale, the local neighborhood is warped by $M^{1/2}$ so that the eigenvalues of the second moment matrix become equal. In the normalized coordinate frame, the spatial position, integration scale, and differentiation scale are updated, and $M$ is recomputed. This process repeats iteratively until the ratio of eigenvalues of $M$ converges to 1 within a tolerance threshold, recovering the affine transformation up to an unknown rotation.
Knowl 4 — Maximally Stable Extremal Region Detector
model/method
The Maximally Stable Extremal Region (MSER) detector extracts connected components of binarized image levels whose geometry remains stable across intensity thresholds.
1. Extremal Regions: For an image $I: \Omega \to \mathbb{R}$ , an extremal region $Q \subset \Omega$ is a contiguous connected component such that for all boundary pixels $q \in \partial Q$ and all interior pixels $p \in Q$ , either $I(p) > I(q)$ (bright extremal region) or $I(p) < I(q)$ (dark extremal region).
2. Stability Criterion: Let $Q(t)$ denote the extremal connected component obtained by thresholding at intensity $t$ . Stability is quantified by the relative area growth rate across a threshold step $\Delta$ : $q(t) = \frac{|Q(t + \Delta) \setminus Q(t - \Delta)|}{|Q(t)|}$ An extremal region $Q(t^*)$ is defined as a maximally stable extremal region if $q(t)$ achieves a local minimum at $t^*$ .
3. Invariance Properties: Because the set of extremal regions depends solely on the relative sorting order of pixel intensities, MSERs are strictly invariant under any continuous monotonic photometric mapping $I' = f(I)$ (including non-linear gamma corrections). Furthermore, MSERs preserve topology under continuous geometric transformations and homographies.
4. Elliptical Representation: To enable standardized descriptor computation and benchmarking, each detected arbitrarily shaped region $Q$ is represented by an equivalent ellipse having the identical first-order centroid and second-order central spatial moments.
5. Complexity: MSER detection is implemented in $O(n)$ time for 8-bit pixel sorting (using bin sort) plus $O(n \log \log n)$ time for component tree tracking using a Union-Find disjoint-set data structure.
Knowl 5 — Edge-Based Region Detector
model/method
The Edge-Based Region (EBR) detector extracts affine covariant regions by exploiting the geometric constraints of corners and adjacent edge contours.
1. Feature Extraction: Multi-scale Harris corner points $\mathbf{p}$ and Canny edge curves are detected in the image.
2. 1D Affine Invariant Edge Traversal: Two points $\mathbf{p}_1(s_1)$ and $\mathbf{p}_2(s_2)$ traverse the edge away from corner $\mathbf{p}$ in opposite directions along edge parameter $s_i$ . Their traversal speeds are synchronized by equalizing the relative affine-invariant area parameters $l_1 = l_2 = l$ : $l_i = \int \left| \mathbf{p}_i^{(1)}(s_i) \times (\mathbf{p} - \mathbf{p}_i(s_i)) \right| ds_i$ where $\mathbf{p}_i^{(1)}(s_i)$ is the first derivative with respect to arc parameter $s_i$ , and $|\cdot \times \cdot|$ denotes the 2D cross-product determinant.
3. Parallelogram Selection via Photometric Invariants: For each parameter value $l$ , vectors $(\mathbf{p}_1(l) - \mathbf{p})$ and $(\mathbf{p}_2(l) - \mathbf{p})$ define a parallelogram $\Omega(l)$ . Photometric moment invariants are evaluated over $\Omega(l)$ : $\text{Inv}_1 = \left| \frac{(\mathbf{p}_1 - \mathbf{p}_g) \times (\mathbf{p}_2 - \mathbf{p}_g)}{(\mathbf{p} - \mathbf{p}_1) \times (\mathbf{p} - \mathbf{p}_2)} \right| \frac{M_{00}^1}{\sqrt{M_{00}^2 M_{00}^0 - (M_{00}^1)^2}}$ $\text{Inv}_2 = \left| \frac{(\mathbf{p} - \mathbf{p}_g) \times (\mathbf{q} - \mathbf{p}_g)}{(\mathbf{p} - \mathbf{p}_1) \times (\mathbf{p} - \mathbf{p}_2)} \right| \frac{M_{00}^1}{\sqrt{M_{00}^2 M_{00}^0 - (M_{00}^1)^2}}$ where $M_{pq}^n = \iint_{\Omega(l)} I^n(x, y) x^p y^q \, dx dy$ , $\mathbf{p}_g = \left(\frac{M_{10}^1}{M_{00}^1}, \frac{M_{01}^1}{M_{00}^1}\right)$ is the intensity-weighted center of gravity, and $\mathbf{q}$ is the corner vertex opposite to $\mathbf{p}$ . Parallelograms where these invariants attain local extrema are selected and fitted with their moment-equivalent ellipses.
Knowl 6 — Intensity Extrema-Based Region Detector
model/method
The Intensity Extrema-Based Region (IBR) detector extracts affine covariant regions by analyzing 1D intensity profiles along rays emanating radially from local intensity extrema.
1. Extrema Detection: Local intensity extrema $\mathbf{x}_0$ with intensity $I_0 = I(\mathbf{x}_0)$ are detected across multiple scales.
2. Radial Profile Invariant Function: Rays are projected outward from $\mathbf{x}_0$ in all directions. Along each ray parameterized by arc parameter $t$ , the following invariant function is computed: $f_I(t) = \frac{|I(t) - I_0|}{\max\left(\frac{1}{t} \int_0^t |I(t') - I_0| \, dt', \, d\right)}$ where $d > 0$ is a small regularization constant preventing division by zero. The parameter $t$ where $f_I(t)$ reaches a local maximum identifies a sharp, affine-invariant boundary transition along that ray direction.
3. Region Delineation and Ellipse Fitting: The boundary points corresponding to the extrema of $f_I(t)$ across all rays are linked to delineate an irregularly shaped closed region. The final region is represented by an ellipse having the identical first- and second-order moments as the delineated region, which preserves affine covariance.
Knowl 7 — Salient Region Detector
model/method
The Salient Region detector identifies affine covariant regions by measuring the entropy of the local intensity probability distribution across scale and affine shape parameters.
1. Local Intensity Entropy: For each pixel $\mathbf{x}$ , candidate elliptical windows $\mathcal{E}$ parameterized by scale $s$ (major axis length), orientation $\theta$ , and axis ratio $\lambda$ are constructed. The Shannon entropy of the intensity probability density function $p(I; s, \theta, \lambda)$ within $\mathcal{E}$ is: $\mathcal{H}(s, \theta, \lambda) = -\sum_I p(I; s, \theta, \lambda) \log p(I; s, \theta, \lambda)$
2. Scale Extrema Search: For every pixel and shape configuration $(\theta, \lambda)$ , scale values $s^*$ where entropy $\mathcal{H}$ attains a local extremum over scale $s$ are selected as candidate salient regions.
3. Saliency Weighting and Ranking: Each candidate region is assigned a saliency score $\mathcal{Y} = \mathcal{H} \cdot \mathcal{W}$ , where $\mathcal{W}$ weights the entropy by the magnitude of the scale derivative of the probability distribution: $\mathcal{W} = \frac{s^2}{2s - 1} \sum_I \left| \frac{\partial p(I; s, \theta, \lambda)}{\partial s} \right|$ All candidate regions across the image are ranked by their saliency $\mathcal{Y}$ , and the top $P$ regions are selected.

Knowl 8 — Computational Complexity and Runtime of Affine Region Detectors

data/table

Execution runtimes and region counts were measured on an $800 \times 640$ image on a 2.0 GHz Pentium 4 Linux PC using default author parameters:

Detector	Run time (min:sec)	Number of regions
Harris-Affine	0:01.43	1791
Hessian-Affine	0:02.73	1649
MSER	0:00.66	533
IBR	0:10.82	679
EBR	2:44.59	1265
Salient Regions	33:33.89	513

Theoretical computational complexities across detectors are:

MSER: $O(n)$ for initial pixel sorting via bin sort plus $O(n \log \log n)$ for connected component tracking with union-find, resulting in sub-second execution.
Harris-Affine and Hessian-Affine: $O(n)$ for initial interest point extraction, followed by $O((m + k)p)$ for automatic scale selection across $m$ scales and $k$ shape adaptation iterations over $p$ points.
IBR: $O(n)$ for extrema detection plus $O(p)$ for ray-based boundary construction over $p$ extrema.
EBR: $O(n)$ for corner and Canny edge extraction plus $O(pd)$ for edge tracing across $p$ corners with an average of $d$ nearby edges.
Salient Regions: $O(n \cdot l)$ for testing $l$ discretized ellipse geometries per pixel, plus $O(e)$ for ranking $e$ candidate extrema.

Knowl 9 — Comparative Repeatability of Affine Detectors Under Image Transformations
empirical result
Empirical evaluation across test sequences spanning structured (planar surfaces with distinct contours) and textured scenes under five transformation types demonstrates:
- Viewpoint Variation: Viewpoint tilt (from $20^\circ$ to $60^\circ$ ) represents the most severe degradation, with repeatability declining from 40%–78% at $20^\circ$ to 10%–46% at $60^\circ$ . MSER achieves the highest percentage repeatability across both structured and textured scenes due to high boundary localization accuracy. Hessian-Affine and Harris-Affine produce the highest absolute number of correct correspondences (1200–1300 at $20^\circ$ , dropping to 200–400 at $60^\circ$ ).
- Scale Change and Zoom: For scale changes up to $4\times$ combined with in-plane rotation, Hessian-Affine achieves the highest repeatability, followed by MSER and Harris-Affine, confirming the robustness of Laplacian-based characteristic scale selection. EBR fails on textured scenes ( $<20\%$ repeatability) due to a lack of stable long edges.
- Image Blur: All detectors demonstrate high blur invariance with nearly horizontal repeatability curves, except MSER. MSER repeatability drops significantly under severe blur because blurred edges degrade the stability of intensity-thresholded component boundaries.
- JPEG Compression and Illumination: Hessian-Affine and Harris-Affine achieve the highest repeatability under JPEG compression (up to 95%). All detectors maintain stable, near-constant repeatability across illumination changes induced by camera aperture variation, with MSER achieving the highest percentage score.
Knowl 10 — Trade-offs in Region Distinctiveness and Matching Precision
empirical result
Matching experiments using 128-dimensional SIFT descriptors reveal systematic differences between affine detector types:
1. High Precision at Low Match Counts (MSER and IBR): MSER and IBR detect sparse, distinct, non-overlapping regions. When matching candidate regions by nearest-neighbor distance in SIFT feature space, over $90\%$ of the top 100 returned matches are geometrically correct (overlap error $\epsilon_O \le 0.40$ ). These detectors are optimal for applications requiring a minimal set of highly accurate correspondences (e.g., estimating two-view epipolar geometry without extensive filtering).
2. High Region Density with Redundancy (Hessian-Affine and Harris-Affine): Hessian-Affine and Harris-Affine extract dense region sets (~1600–1800 detections per image), frequently producing multiple slightly shifted or differently scaled elliptical detections centered on the same local image structure. Because competing detections have similar descriptor representations, nearest-neighbor descriptor matching generates higher false positive rates at tight descriptor distance thresholds. However, they provide significantly more total correct matches (over 200 matches) when geometric filtering or RANSAC verification is applied, making them superior in cluttered or heavily occluded scenes.

Coverage note — None was omitted; all six affine region detector formulations, the benchmarking protocol, experimental parameters, complexity analyses, and empirical findings are fully covered.

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Citation

MLA

Mikolajczyk, K., et al. “A Comparison of Affine Region Detectors”. International Journal of Computer Vision, vol. 65, nos. 1-2, 2005, pp. 43–72, https://doi.org/10.1007/s11263-005-3848-x.

APA

Mikolajczyk, K., Tuytelaars, T., Schmid, C., Zisserman, A., Matas, J., Schaffalitzky, F., Kadir, T., & Gool, L. V. (2005). A Comparison of Affine Region Detectors. International Journal of Computer Vision, 65(1-2), 43–72. https://doi.org/10.1007/s11263-005-3848-x

Chicago

Mikolajczyk, K., T. Tuytelaars, C. Schmid, et al. 2005. “A Comparison of Affine Region Detectors”. International Journal of Computer Vision 65 (1-2): 43–72. https://doi.org/10.1007/s11263-005-3848-x.

Harvard

Mikolajczyk, K. et al. (2005) “A Comparison of Affine Region Detectors”, International Journal of Computer Vision, 65(1-2), pp. 43–72. Available at: https://doi.org/10.1007/s11263-005-3848-x.

Vancouver

1. Mikolajczyk K, Tuytelaars T, Schmid C, Zisserman A, Matas J, Schaffalitzky F, Kadir T, Gool LV (2005) A Comparison of Affine Region Detectors. International Journal of Computer Vision 65:43–72

BibTeX

@article{Mikolajczyk_2005, title={A Comparison of Affine Region Detectors}, volume={65}, ISSN={1573-1405}, url={http://dx.doi.org/10.1007/s11263-005-3848-x}, DOI={10.1007/s11263-005-3848-x}, number={1-2}, journal={International Journal of Computer Vision}, publisher={Springer Science and Business Media LLC}, author={Mikolajczyk, K. and Tuytelaars, T. and Schmid, C. and Zisserman, A. and Matas, J. and Schaffalitzky, F. and Kadir, T. and Gool, L. Van}, year={2005}, month=Oct, pages={43–72} }

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A Comparison of Affine Region Detectors

Abstract

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Knowls

Knowl 1 — Overlap Error and Repeatability Evaluation Metric for Affine Region Detectors

Knowl 2 — SIFT-Based Matching Score Metric for Affine Covariant Regions

Knowl 3 — Harris-Affine and Hessian-Affine Detectors

Knowl 4 — Maximally Stable Extremal Region Detector

Knowl 5 — Edge-Based Region Detector

Knowl 6 — Intensity Extrema-Based Region Detector

Knowl 7 — Salient Region Detector

Knowl 8 — Computational Complexity and Runtime of Affine Region Detectors

Knowl 9 — Comparative Repeatability of Affine Detectors Under Image Transformations

Knowl 10 — Trade-offs in Region Distinctiveness and Matching Precision

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