Evaluation of Interest Point Detectors

CORDELIA SCHMIDROGER MOHRCHRISTIAN BAUCKHAGE

article2000IJCV1,781 citations

Establishes a rigorous benchmarking framework using repeatability rate and information content to quantitatively determine which interest point detectors provide the highest geometric stability and feature distinctiveness across varying imaging conditions.

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Many computer vision applications—such as image matching, 3D scene reconstruction, and automated object recognition—depend heavily on the reliable extraction of low-level visual features known as interest points. Historically, evaluating these detectors relied on subjective human visual inspections, narrow feature models, or application-specific pipelines that were difficult to generalize. Because the choice of detector dramatically alters system performance, developers need objective, generalizable benchmarks to choose the best algorithms for multi-image processing tasks.

The article establishes two rigorous, automated evaluation criteria—repeatability rate and information content—to quantitatively assess and rank leading interest point detectors across realistic operating conditions.

The evaluation framework tests detectors across two fundamental dimensions. First, repeatability measures the geometric stability of detected points across changing physical imaging conditions, including image rotations, scale changes, lighting variations, viewpoint shifts, and camera sensor noise. Geometric ground truth is established on static scenes using projective transformations calculated via independently projected calibration patterns. Second, information content evaluates the distinctiveness of local image patterns around detected points using entropy measurements across a dataset of 1,000 diverse images (aerial scenes, paintings, and objects) to quantify how well these features prevent ambiguity during matching.

The experimental results identify an improved version of the Harris detector—implemented with stable Gaussian derivative filters—as the top-performing method overall. Under image rotations, this improved detector maintains nearly a 100% repeatability rate within a 1.5-pixel error margin, completely eliminating the 45-degree performance dips seen in standard discrete implementations. Across viewpoint changes, it consistently maintains repeatability above 60%, significantly outperforming contour-based and model-based alternatives. In distinctiveness evaluations, the improved Harris detector achieved the highest entropy score (6.05), followed closely by the biologically inspired Heitger detector (5.94), whereas contour-only detectors scored noticeably lower and random points produced an entropy of only 3.30 (making false feature collisions roughly 15.6 times more likely). Across all detectors, scale changes proved to be the most severe vulnerability, with repeatability collapsing rapidly when image scale varied by a factor of 1.5 to 2.0 or greater.

These findings provide clear practical guidelines for system designers. Selecting an interest point detector that maximizes both repeatability and information content substantially lowers the risk of feature mismatching, reduces downstream computational overhead, and improves tracking stability. The results also show that relying strictly on image contours degrades overall feature distinctiveness, and using unaligned directional derivative filters introduces hidden geometric vulnerabilities when images rotate.

For immediate deployment in matching and tracking pipelines, the article recommends using the improved Gaussian-based Harris detector. To overcome the universal limitation of scale sensitivity, engineering teams should incorporate these interest point operators into multi-scale frameworks or implement explicit scale-selection mechanisms before applying them to scenes with large zoom or distance changes.

Confidence in these findings is high for planar and general surface matching under rotation, lighting changes, and moderate viewpoint variations. However, decision-makers should note that the geometric ground-truth validation is mathematically constrained to planar scenes to avoid confounding detector performance with physical occlusions and shadow boundaries that naturally occur in complex 3D environments.

INRIA detection algorithm information contents interest points interest point detectors detector evaluation corner detectors

SCHMID et al (2000).pdf

Paper: Local Grayvalue Invariants for Image Retrieval, Cordelia Schmid et al. (1997). Introduces local grayvalue invariants at interest points for image matching and retrieval, establishing the foundational local-feature paradigm evaluated and benchmarked in the source paper.
Paper: Feature Detection with Automatic Scale Selection, Tony Lindeberg (1998). Develops the principles of automatic scale selection and differential scale-space feature detection that underpin multi-scale interest point formulation and evaluation.

Paper: Scale & Affine Invariant Interest Point Detectors, K. Mikolajczyk et al. (2004). Builds directly on the repeatability evaluation methodology to develop and validate scale- and affine-invariant interest point detectors such as Harris-Laplace.
Paper: A Comparison of Affine Region Detectors, K. Mikolajczyk et al. (2005). Extends the source's evaluation framework to affine-covariant region detectors using homography-based repeatability and descriptor matching benchmarks.
Paper: A performance evaluation of local descriptors, Krystian Mikolajczyk et al. (2005). Complements interest point detector evaluation by establishing a systematic benchmark for the local descriptors extracted around those detected points.
Paper: Distinctive Image Features from Scale-Invariant Keypoints, David G. Lowe (2004). Presents scale-invariant feature transform (SIFT) keypoint detection and description, heavily relying on repeatability and distinctiveness criteria established in earlier feature evaluation work.
Paper: Machine Learning for High-Speed Corner Detection, Edward Rosten et al. (2006). Uses the repeatability metric formalized in interest point evaluation benchmarks to design and evaluate the high-speed FAST corner detector.
Paper: SURF: Speeded Up Robust Features, Herbert Bay et al. (2006). Introduces SURF as an accelerated scale- and rotation-invariant detector-descriptor pair evaluated against standard repeatability and distinctiveness protocols.
Paper: On Space-Time Interest Points, I. Laptev (2005). Generalizes the spatial interest point concept and scale selection principles into the spatio-temporal domain for video event representation.
Paper: SuperPoint: Self-Supervised Interest Point Detection and Description, Daniel DeTone et al. (2017). Revisits repeatable interest point detection in a modern deep learning framework using self-supervised homographic adaptation.

Cover for Evaluation of Interest Point Detectors

Abstract

Many different low-level feature detectors exist and it is widely agreed that the evaluation of detectors is important. In this paper we introduce two evaluation criteria for interest points: repeatability rate and information content. Repeatability rate evaluates the geometric stability under different transformations. Information content measures the distinctiveness of features. Different interest point detectors are compared using these two criteria. We determine which detector gives the best results and show that it satisfies the criteria well.

Topics

detection algorithm information contents interest points

Keywords

interest point detectors detector evaluation corner detectors Harris detector point descriptors corner detection localization accuracy Heitger detector image matching object recognition

1. Introduction
1.1. Related Work on the Evaluation of Feature Detectors
1.2. Overview of the Paper
2. Interest Point Detectors
2.1. State of the Art
2.2. Implementation Details
3. Repeatability
3.1. Repeatability Criterion
3.2. Experimental Conditions
3.3. Results for Repeatability
3.4. Conclusion for Repeatability
4. Information Content
4.1. Information Content Criterion
4.2. Entropy
4.3. Descriptors Characterizing Local Shape
4.4. Partitioning a Set of Descriptors
4.5. Results for Information Content
5. Conclusion
Appendix A: Derivation of the Auto-Correlation Matrix
Appendix B: Repeatability Results for the 'Asterix' Scene
B.1. Comparison of the Two Harris Versions
B.2. Image Rotation
B.3. Scale Change
B.4. Uniform Variation of Illumination
B.5. Camera Noise
Acknowledgments
References

Knowls

Knowl 1 — Repeatability Rate Criterion for Interest Point Evaluation
definition
The repeatability rate measures the geometric stability of an interest point detector when a static scene is imaged under changing viewing conditions (such as varying camera viewpoint, rotation, scale, illumination, or sensor noise). For a planar 3D scene imaged across two views $I_1$ and $I_i$ with camera projection matrices $P_1$ and $P_i$ , the geometric mapping between corresponding image points $x_1 = P_1 X$ and $x_i = P_i X$ is defined by a planar homography:
$x_i = H_{1i} x_1 \quad \text{where} \quad H_{1i} = P_i P_1^{-1}$
where $H_{1i}$ is the $3 \times 3$ homography matrix mapping homogeneous coordinates from $I_1$ to $I_i$ , and $H_{i1} = H_{1i}^{-1}$ .

To ensure that points outside the shared field of view do not distort the evaluation, only interest points situated within the overlapping scene area are evaluated:
$\{\tilde{x}_1\} = \{x_1 \in \{x_1\} \mid H_{1i} x_1 \in I_i\} \quad \text{and} \quad \{\tilde{x}_i\} = \{x_i \in \{x_i\} \mid H_{i1} x_i \in I_1\}$
where $\{x_1\}$ and $\{x_i\}$ are the raw sets of interest points detected in $I_1$ and $I_i$ , respectively.

Given a localization error tolerance $\epsilon > 0$ (in pixels), the set of $\epsilon$ -repeated point pairs $R_i(\epsilon)$ is:
$R_i(\epsilon) = \{ (\tilde{x}_1, \tilde{x}_i) \in \{\tilde{x}_1\} \times \{\tilde{x}_i\} \mid \operatorname{dist}(H_{1i} \tilde{x}_1, \tilde{x}_i) < \epsilon \}$
where $\operatorname{dist}(\cdot, \cdot)$ is the Euclidean distance in the coordinate frame of image $I_i$ .

The repeatability rate $r_i(\epsilon)$ is defined as the number of repeated points divided by the minimum number of detected points in the common scene part:
$r_i(\epsilon) = \frac{|R_i(\epsilon)|}{\min(n_1, n_i)}$
where $n_1 = |\{\tilde{x}_1\}|$ and $n_i = |\{\tilde{x}_i\}|$ . The rate satisfies $0 \le r_i(\epsilon) \le 1$ .
Knowl 2 — Information Content Criterion for Interest Points
definition
Information content measures the distinctiveness of a detector's extracted interest points based on the distribution of their local greyvalue descriptors across the descriptor space. If interest point descriptors cluster closely together, the features lack distinctiveness and matching algorithms (such as correlation or nearest-neighbor feature matching) will suffer from severe ambiguity. If descriptors are widely spread across the descriptor space, distinctiveness is high.

For a set of interest points detected across an image collection, a local greyvalue descriptor vector $\vec{v} \in \mathbb{R}^d$ is computed at each interest point. The descriptor space is partitioned into a discrete set of disjoint cells $\mathcal{A} = \{A_k\}$ . The information content is defined as the Shannon entropy of this partition:
$H(\mathcal{A}) = -\sum_k p_k \log(p_k)$
where $p_k$ is the empirical probability that a detected interest point descriptor falls into cell $A_k$ . Higher entropy corresponds to a higher average information content per feature and greater distinctiveness.
Knowl 3 — Second-Order Local Jet Differential Invariant Descriptors
model/method
To characterize local image geometry at interest points independently of 2D image rotations (invariance under $SO(2)$ ), descriptors are constructed from combinations of Gaussian image derivatives up to second order (the local jet).

Let $I(x, y)$ be the image intensity surface and $L_{i_1 \dots i_n}(x, y, \sigma) = I * G_{i_1 \dots i_n}(x, y, \sigma)$ denote the convolution of $I$ with the $n$ -th partial Gaussian derivative kernel at scale $\sigma$ , with $i_k \in \{x, y\}$ . The four-dimensional rotation-invariant descriptor $\vec{v} = (v_0, v_1, v_2, v_3)^T$ computed at scale $\sigma$ (omitting zeroth-order average luminance to ensure illumination invariance) is defined by:
$\vec{v} = \begin{bmatrix} L_x^2 + L_y^2 \\ L_{xx} L_x^2 + 2 L_{xy} L_x L_y + L_{yy} L_y^2 \\ L_{xx} + L_{yy} \\ L_{xx}^2 + 2 L_{xy}^2 + L_{yy}^2 \end{bmatrix}$
The components correspond to standard differential invariants:
- $v_0$ is the squared gradient magnitude.
- $v_1$ represents the directional second derivative along the gradient direction weighted by the gradient magnitude.
- $v_2$ is the Laplacian of the Gaussian-smoothed image.
- $v_3$ is the squared Frobenius norm of the Hessian matrix.
Knowl 4 — Mahalanobis Partitioning Algorithm for Descriptor Entropy Evaluation
algorithm
To compute the entropy of continuous differential invariant descriptors $\vec{v} \in \mathbb{R}^4$ , the descriptor space is normalized to account for descriptor noise covariance and then partitioned into uniform hypercube bins.

The procedure runs as follows:
Input: Set of descriptor vectors $V = \{\vec{v}_j\}_{j=1}^M \subset \mathbb{R}^d$ , bin width parameter $w$ ( $w = 20$ )
Output: Information content entropy $H(\mathcal{A})$
Compute sample mean $\bar{\vec{v}} = \frac{1}{M} \sum_{j=1}^M \vec{v}_j$
Compute sample covariance matrix $\Lambda = \frac{1}{M} \sum_{j=1}^M (\vec{v}_j - \bar{\vec{v}})(\vec{v}_j - \bar{\vec{v}})^T$
Compute eigendecomposition of the inverse covariance matrix $\Lambda^{-1} = P^T D P$ , where $P$ is orthogonal and $D$ is diagonal with positive eigenvalues
Form whitening transformation matrix $T = D^{1/2} P$
For each vector $\vec{v}_j \in V$ :
    Compute normalized descriptor $\vec{v}_{\text{norm}, j} = T \vec{v}_j$
    Compute grid cell coordinate $\mathbf{k}_j = \lfloor \vec{v}_{\text{norm}, j} / w \rfloor \in \mathbb{Z}^d$
Count the number of descriptors $c(\mathbf{k})$ assigned to each unique grid cell $\mathbf{k}$
For each occupied cell $\mathbf{k}$ :
    Compute probability $p(\mathbf{k}) = c(\mathbf{k}) / M$
Compute entropy $H(\mathcal{A}) = -\sum_{\mathbf{k}} p(\mathbf{k}) \log(p(\mathbf{k}))$
return $H(\mathcal{A})$
The Mahalanobis distance between raw descriptors matches the Euclidean distance between normalized descriptors: $d_M(\vec{v}_1, \vec{v}_2) = \| \vec{v}_{\text{norm}, 1} - \vec{v}_{\text{norm}, 2} \|_2$ , ensuring that equal-sized cubic bins in normalized space reflect uniform probability densities under isotropic noise.
Knowl 5 — Improved Harris Detector (ImpHarris)
model/method
The standard Harris detector uses a discrete difference filter $[-2, -1, 0, 1, 2]$ to compute image derivatives, creating directional bias that significantly degrades repeatability under image rotation. The improved Harris detector (ImpHarris) replaces the discrete mask with isotropic Gaussian derivative filters.

The detection pipeline consists of:
1. Gradient computation: Image derivatives $I_x, I_y$ are computed by convolving the image with first-order Gaussian derivative filters at differentiation scale $\sigma_D = 1.0$ (implemented via Deriche recursive filters for speed).
2. Structure tensor integration: The auto-correlation matrix $A(x, y)$ is computed by Gaussian smoothing over an integration neighborhood at scale $\sigma_I = 2.0$ :
$A(x, y) = G(\sigma_I) * \begin{bmatrix} I_x(x, y)^2 & I_x(x, y) I_y(x, y) \\ I_x(x, y) I_y(x, y) & I_y(x, y)^2 \end{bmatrix}$
1. Corner strength measurement: The corner response is computed as:
$R(x, y) = \det(A(x, y)) - \alpha \, (\operatorname{trace}(A(x, y)))^2$
with $\alpha = 0.06$ . 4. Non-maximum suppression: Local maxima of $R(x, y)$ are detected using a $3 \times 3$ window. 5. Thresholding: Points with corner strength below $1\%$ of the maximum observed corner response in the image are discarded.
Knowl 6 — Ground-Truth Homography Estimation via Projected Dot Grid
experimental setup
To evaluate interest point repeatability without relying on the detector outputs or subjective human ground truth, ground-truth homographies between image pairs are obtained via an independent sub-pixel calibration target.

For every camera position and illumination setting on a static planar scene:
1. A primary test image of the unmodified scene is acquired.
2. A secondary calibration image is acquired without moving the camera, during which an overhead projector at a fixed location casts an array of discrete black dots onto the scene.
The dot centers in the calibration images are localized to sub-pixel accuracy by template fitting. The inter-image homography $H_{1i}$ relating reference image $I_1$ to image $I_i$ is computed from the matched dot coordinates using a robust Least Median of Squares (LMedS) estimator. Because the projector remains fixed throughout camera motion, dot positions provide objective, sub-pixel ground-truth homographies that are completely decoupled from the feature extraction algorithms under test.

Knowl 7 — Information Content of Interest Point Detectors

data/table

The information content of interest point detectors was evaluated across a diverse collection of 1,000 images (aerial images, paintings, and toy objects). Second-order differential invariant descriptors were extracted at scale $\sigma = 3$ , normalized using Mahalanobis whitening, binned into cubic cells of width 20, and their Shannon entropy calculated. A random baseline was obtained by uniformly sampling $m$ points per image, where $m$ matched the average number of points extracted by the evaluated detectors.

The measurements show:

ImpHarris yields the highest entropy ( $6.05$ ), indicating the greatest diversity and distinctiveness in local appearance patterns.
Heitger is a close second ( $5.94$ ).
Detectors constrained to edge contours (Cottier at $4.85$ , Horaud at $5.43$ ) produce lower entropy because restricting interest points to 1D contours limits the diversity of surrounding 2D intensity patterns.
All detectors significantly exceed random point selection ( $3.30$ ). The probability of two randomly selected points sharing the same descriptor bin is $e^{-(3.30 - 6.05)} \approx 15.6$ times higher than for points detected by ImpHarris.

Knowl 8 — Repeatability Performance Under Rotation and Viewpoint Variation
empirical result
Under 2D in-plane image rotations ranging from $0^\circ$ to $180^\circ$ :
- ImpHarris achieves the highest repeatability, maintaining approximately $90\%$ to $100\%$ repeatability at localization tolerance $\epsilon = 1.5$ pixels and $\sim 40\%$ at $\epsilon = 0.5$ pixels uniformly across all rotation angles.
- The standard Harris detector suffers periodic degradation in repeatability at $45^\circ$ rotation increments due to the anisotropy of its $[-2, -1, 0, 1, 2]$ derivative filter.
- Detectors combining directional 1D filter responses (Heitger) or anisotropic filters (F"orstner) degrade significantly between $40^\circ$ and $140^\circ$ .
- Line-intersection corner extraction (Horaud) yields the lowest rotation repeatability ( $\\sim 20-30\%$ at $\epsilon = 1.5$ ).
Under out-of-plane perspective viewpoint changes spanning camera angles from $-50^\circ$ to $+50^\circ$ :
- ImpHarris maintains superior repeatability over all competing detectors, exceeding $60\%$ repeatability across almost the entire angular range for $\epsilon = 1.5$ pixels.
- Tight localization requirements ( $\epsilon = 0.5$ pixels) degrade rapidly under perspective distortion, while an error tolerance of $\epsilon = 1.5$ pixels preserves robust correspondence.
Knowl 9 — Scale Sensitivity Limitation of Fixed-Scale Interest Point Detectors
empirical result
Interest point detectors utilizing fixed-size derivative and smoothing filters (including ImpHarris, Cottier, F"orstner, Heitger, and Horaud) degrade rapidly in the presence of camera zoom and scale changes.

Empirical evaluation across focal length scale factors from $1.0$ to $4.5$ shows:
- At localization tolerance $\epsilon = 0.5$ pixels, repeatability drops precipitously for scale factors exceeding $1.5$ .
- At $\epsilon = 1.5$ pixels, repeatability drops sharply beyond a scale factor of $2.0$ (for ImpHarris, repeatability drops from $\sim 85\%$ at scale factor $1.0$ to $54\%$ at scale factor $1.5$ , $\sim 25\%$ at scale factor $2.0$ , and below $5\%$ for scale factors greater than $3.0$ ).
- Beyond a scale factor of approximately $2.5$ , detected correspondences are largely accidental matches caused by high point density in high-resolution texture areas.
- ImpHarris and Cottier outperform other detectors under small scale changes, but no fixed-scale detector maintains practical repeatability under scale variations greater than a factor of $2$ .
Knowl 10 — Repeatability Under Illumination Variation and Camera Noise
empirical result
Under uniform illumination variation (adjusting camera aperture over relative mean greyvalue ratios of $0.6$ to $1.7$ relative to nominal illumination):
- Repeatability decreases smoothly and symmetrically as brightness deviates from nominal levels, with ImpHarris and Heitger achieving the highest stability ( $> 85-90\%$ repeatability at $\epsilon = 1.5$ pixels across moderate illumination shifts).
Under complex, non-uniform illumination changes (moving a light source along an arc of $-45^\circ$ to $+45^\circ$ causing moving directional shadows and localized saturation):
- ImpHarris maintains nearly constant repeatability ( $\\sim 90\%$ at $\epsilon = 1.5$ pixels across all light source angles), indicating that localized gradient auto-correlation is largely invariant to illumination direction, whereas contour-intersection detectors (Horaud) fall to $30-40\%$ .
Under camera sensor noise across repeated static scene captures:
- ImpHarris and Heitger achieve nearly $100\%$ repeatability at $\epsilon = 1.5$ pixels and $\sim 90\%$ at $\epsilon = 0.5$ pixels, outperforming F"orstner ( $75-80\%$ ) and Horaud ( $45\%$ ).

Coverage note — Previous literature review of existing corner/edge detectors and duplicate experimental repeatability curves for the secondary Asterix scene in Appendix B (which yielded identical comparative conclusions to the primary Van Gogh dataset) were omitted.

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Citation

MLA

Schmid, C., et al. “Evaluation of Interest Point Detectors”. International Journal of Computer Vision, vol. 37, no. 2, 2000, pp. 151–72, https://doi.org/10.1023/A:1008199403446.

APA

Schmid, C., Mohr, R., & Bauckhage, C. (2000). Evaluation of Interest Point Detectors. International Journal of Computer Vision, 37(2), 151–172. https://doi.org/10.1023/A:1008199403446

Chicago

Schmid, C., R. Mohr, and C. Bauckhage. 2000. “Evaluation of Interest Point Detectors”. International Journal of Computer Vision 37 (2): 151–72. https://doi.org/10.1023/A:1008199403446.

Harvard

Schmid, C., Mohr, R. and Bauckhage, C. (2000) “Evaluation of Interest Point Detectors”, International Journal of Computer Vision, 37(2), pp. 151–172. Available at: https://doi.org/10.1023/A:1008199403446.

Vancouver

1. Schmid C, Mohr R, Bauckhage C (2000) Evaluation of Interest Point Detectors. International Journal of Computer Vision 37:151–172

BibTeX

@article{Schmid_2000, title={Evaluation of Interest Point Detectors}, volume={37}, ISSN={1573-1405}, url={http://dx.doi.org/10.1023/A:1008199403446}, DOI={10.1023/a:1008199403446}, number={2}, journal={International Journal of Computer Vision}, publisher={Springer Science and Business Media LLC}, author={Schmid, Cordelia and Mohr, Roger and Bauckhage, Christian}, year={2000}, month=June, pages={151–172} }

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Detector	Information content
ImpHarris	6.049526
Heitger	5.940877
Horaud	5.433776
Cottier	4.846409
Förstner	4.523368
Random	3.300863

Evaluation of Interest Point Detectors

Abstract

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Table of Contents

Knowls

Knowl 1 — Repeatability Rate Criterion for Interest Point Evaluation

Knowl 2 — Information Content Criterion for Interest Points

Knowl 3 — Second-Order Local Jet Differential Invariant Descriptors

Knowl 4 — Mahalanobis Partitioning Algorithm for Descriptor Entropy Evaluation

Knowl 5 — Improved Harris Detector (ImpHarris)

Knowl 6 — Ground-Truth Homography Estimation via Projected Dot Grid

Knowl 7 — Information Content of Interest Point Detectors

Knowl 8 — Repeatability Performance Under Rotation and Viewpoint Variation

Knowl 9 — Scale Sensitivity Limitation of Fixed-Scale Interest Point Detectors

Knowl 10 — Repeatability Under Illumination Variation and Camera Noise

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