Faster and Better: A Machine Learning Approach to Corner Detection

Edward RostenReid PorterTom Drummond

article2008TPAMI2,008 citations

Proposes a machine-learning-derived corner detector that achieves superior repeatability over standard methods like Harris and SIFT while consuming less than five percent of available processing time on live video.

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Real-time computer vision applications, such as robotic mapping, object tracking, and augmented reality, require rapid and reliable detection of visual interest points or corners across changing camera viewpoints. Conventional corner detectors demand substantial computational power, often consuming the majority or entirety of available processing time. This computational bottleneck leaves insufficient resources for subsequent analysis and severely constrains performance on low-power devices.

The article evaluates whether machine learning techniques can optimize heuristic corner detection to achieve real-time frame rates while maintaining or exceeding the detection repeatability of established computer vision algorithms.

To address this, the authors used decision tree induction to optimize a circular segment test heuristic, identifying a contiguous sequence of bright or dark pixels around a candidate point. They generated an ultra-fast detector (FAST-9) and further combined decision tree structures with simulated annealing to create an enhanced detector (FAST-ER) directly optimized for high repeatability. Evaluation was conducted across three-dimensional scenes, bas-relief textures, and standard benchmarks encompassing 85 images and 688 image pairs under diverse viewpoint, scale, blur, lighting, and noise conditions.

The findings show that FAST-9 processes standard video using roughly 5% of the total computational budget, running nearly twice as fast as handwritten implementations and far outperforming conventional alternatives such as Harris (115%) and SIFT Difference-of-Gaussians (195%), which cannot maintain real-time frame rates on standard desktop hardware. FAST-ER achieves the highest overall repeatability score (1313.6) across the evaluation datasets, surpassing established methods including Difference-of-Gaussians (1275.6) and Harris (1195.2). While baseline FAST variants show sensitivity to image noise due to evaluating minimal pixel subsets, FAST-ER exhibits significantly improved noise resilience and maintains steady repeatability across varying feature densities.

These results demonstrate that direct optimization against repeatability criteria can outperform traditional detectors built on human geometric intuition. For engineering and product teams, adopting these machine learning-driven detectors eliminates the processing bottleneck of early-stage vision pipelines. This efficiency enables real-time computer vision on embedded and resource-constrained hardware while freeing computational capacity for downstream tracking and recognition algorithms.

Organizations developing real-time vision systems should adopt FAST-9 when raw execution speed is paramount and implement FAST-ER when maximum feature repeatability and noise robustness are required. Practitioners deploying FAST variants in high-noise environments should carefully calibrate detection thresholds or integrate lightweight pre-filtering. Further application-level benchmarking is recommended to assess downstream tracking performance across domain-specific image datasets.

3d scenes corner detector detection algorithm corner detection corner detector segment test detector

arXiv: 0810.2434 edrosten/fast-er

Paper: Machine Learning for High-Speed Corner Detection, Edward Rosten et al. (2006). This paper establishes the original FAST corner detector and decision-tree learning framework that the source paper directly generalizes, optimizes, and benchmarks.
Paper: Scale & Affine Invariant Interest Point Detectors, K. Mikolajczyk et al. (2004). It provides foundational principles and standardized repeatability evaluation metrics for interest point detectors across geometric variations that the source adopts.
Paper: A Comparison of Affine Region Detectors, K. Mikolajczyk et al. (2005). It introduces standard comparative benchmarking methodologies and repeatability criteria for local feature detectors against which the source evaluates its detector.
Paper: Distinctive Image Features from Scale-Invariant Keypoints, David G. Lowe (2004). It defines the classical SIFT detector and keypoint evaluation baselines that serve as primary comparison points for computational efficiency and detection quality in the source.
Paper: SURF: Speeded Up Robust Features, Herbert Bay et al. (2006). It presents SURF, a prominent accelerated feature detector baseline evaluated in the source paper's comparative analysis of speed versus repeatability.

Paper: BRIEF: Binary Robust Independent Elementary Features, Michael Calonder et al. (2010). It pairs ultra-fast binary intensity tests directly with high-speed keypoint detectors like FAST to achieve fully real-time feature extraction and matching.
Paper: SuperPoint: Self-Supervised Interest Point Detection and Description, Daniel DeTone et al. (2017). It evolves the concept of learned, repeatable interest point detection from decision trees on hand-crafted circle heuristics to deep, self-supervised convolutional networks.
Paper: SuperGlue: Learning Feature Matching With Graph Neural Networks, Paul-Edouard Sarlin et al. (2020). It extends pipelines based on fast local keypoint detectors by replacing classical heuristic matching with learned graph neural network data association.

Cover for Faster and Better: A Machine Learning Approach to Corner Detection

Abstract

The repeatability and efficiency of a corner detector determines how likely it is to be useful in a real-world application. The repeatability is importand because the same scene viewed from different positions should yield features which correspond to the same real-world 3D locations [Schmid et al 2000]. The efficiency is important because this determines whether the detector combined with further processing can operate at frame rate.

Three advances are described in this paper. First, we present a new heuristic for feature detection, and using machine learning we derive a feature detector from this which can fully process live PAL video using less than 5% of the available processing time. By comparison, most other detectors cannot even operate at frame rate (Harris detector 115%, SIFT 195%). Second, we generalize the detector, allowing it to be optimized for repeatability, with little loss of efficiency. Third, we carry out a rigorous comparison of corner detectors based on the above repeatability criterion applied to 3D scenes. We show that despite being principally constructed for speed, on these stringent tests, our heuristic detector significantly outperforms existing feature detectors. Finally, the comparison demonstrates that using machine learning produces significant improvements in repeatability, yielding a detector that is both very fast and very high quality.

Topics

3d scenes corner detector detection algorithm sift tabu search supervised machine learning

Keywords

corner detection corner detector segment test detector corner response curvature estimation feature detection image matching

I Introduction
II Previous work
II-A Corner detectors
II-A1 Edge based corner detectors
II-A2 Greylevel derivative based detectors
II-A3 Direct greylevel detectors
II-B Comparison of feature detectors
III High-speed corner detection
III-A FAST: Features from Accelerated Segment Test
III-B Improving generality and speed with machine learning
III-C Non-maximal suppression
IV Measuring detector repeatability
V FAST-ER: Enhanced Repeatability
V-A Parameters and justification
VI Results
VI-A Repeatability
VI-B Speed
VII Conclusions
References

Knowls

Knowl 1 — Segment Test Criterion for FAST Corner Detection
model/method
The Features from Accelerated Segment Test (FAST) corner detection heuristic identifies corner features in greyscale images using a discretized Bresenham circle of 16 pixels surrounding a candidate pixel $p$ at radius 3. Let $I_p$ denote the intensity of candidate pixel $p$ , and let $I_{p \to x}$ denote the intensity of pixel $x \in \{1, 2, \dots, 16\}$ along the 16-pixel ring around $p$ .

The candidate pixel $p$ is classified as a corner if and only if there exists a set of $n$ contiguous pixels on the circle that are all strictly brighter than $I_p + t$ or all strictly darker than $I_p - t$ , where $t > 0$ is an intensity difference threshold. Formally, $p$ is a corner if there exists a contiguous arc of length $n$ on the 16-pixel ring such that:

$\forall x \in \text{arc}, \quad I_{p \to x} \ge I_p + t$

or

$\forall x \in \text{arc}, \quad I_{p \to x} \le I_p - t$

In the baseline FAST-12 variant ( $n = 12$ ), a rapid preliminary rejection test checks the 4 orthogonal cardinal pixels (positions 1, 5, 9, and 13). If candidate pixel $p$ is a corner, at least three of these four pixels must be simultaneously brighter than $I_p + t$ or darker than $I_p - t$ . If not, $p$ is discarded immediately without evaluating the remaining 12 pixels.
Knowl 2 — Decision Tree Learning for FAST Corner Detection
algorithm
To optimize the execution speed of FAST corner detection for arbitrary segment lengths $n$ , a ternary decision tree classifier is learned from image data using the ID3 decision tree induction algorithm.

For a candidate pixel $p$ and a circle offset $x \in \{1, \dots, 16\}$ , the relative intensity state $S_{p \to x}$ takes one of three discrete values:

$S_{p \to x} = \begin{cases} d & \text{if } I_{p \to x} \le I_p - t \quad (\text{darker}) \\ s & \text{if } I_p - t < I_{p \to x} < I_p + t \quad (\text{similar}) \\ b & \text{if } I_p + t \le I_{p \to x} \quad (\text{brighter}) \end{cases}$

Let $P$ denote the training set of candidate pixels, and let $K_p \in \{0, 1\}$ be a boolean label where $K_p = 1$ if $p$ satisfies the FAST segment test criterion and $K_p = 0$ otherwise. Choosing an offset $x$ partitions $P$ into three disjoint subsets: $P_d = \{p \in P : S_{p \to x} = d\}$ , $P_s = \{p \in P : S_{p \to x} = s\}$ , and $P_b = \{p \in P : S_{p \to x} = b\}$ .

The entropy $H(Q)$ of corner labels in an arbitrary subset $Q \subseteq P$ is defined as:

$H(Q) = (c + \bar{c}) \log_2(c + \bar{c}) - c \log_2 c - \bar{c} \log_2 \bar{c}$

where $c = |\{p \in Q : K_p = 1\}|$ is the number of corners and $\bar{c} = |\{p \in Q : K_p = 0\}|$ is the number of non-corners. The information gain $H_g$ achieved by splitting on offset $x$ is:

$H_g = H(P) - H(P_d) - H(P_s) - H(P_b)$
Input: Training set of pixels $P$ , circle offset space $X = \{1, \dots, 16\}$
Output: Ternary decision tree $T$
function BuildTree(subset $Q$ ):
    if $H(Q) == 0$ :
        return LeafNode(class = majority class of $K_p$ in $Q$ )
     $x^* = \arg\max_{x \in X} H_g(Q, x)$
    Partition $Q$ into $Q_d, Q_s, Q_b$ using $x^*$
     $T_d = \text{BuildTree}(Q_d)$
     $T_s = \text{BuildTree}(Q_s)$
     $T_b = \text{BuildTree}(Q_b)$
    if $T_d == T_s == T_b$ :
        return $T_d$
    return DecisionNode(offset = $x^*$ , dark_branch = $T_d$ , similar_branch = $T_s$ , bright_branch = $T_b$ )
The learned decision tree is converted into optimized C code consisting of nested if-else branches. Profile-guided compiler optimization is applied for branch prediction and block reordering. To enable SIMD vectorization (e.g., SSE-2) across pixel strips, the root node and its three direct child nodes are constrained to test identical offsets ( $x_b = x_d = x_s$ ), enabling the first two pixel tests to run in parallel across multiple pixels.
Knowl 3 — Corner Response Computation and Non-Maximal Suppression for FAST
algorithm
Because the FAST segment test outputs a binary classification rather than a continuous score, corner response values must be computed explicitly to enable non-maximal suppression.

For a fixed segment length $n$ , the corner classification $K_p(t) \in \{0, 1\}$ for candidate pixel $p$ is a monotonically decreasing function of the intensity difference threshold $t$ . The corner strength $V(p)$ is defined as the maximum integer threshold $t$ at which pixel $p$ remains classified as a corner:

$V(p) = \max \{ t \in \mathbb{Z}^+ : K_p(t) = 1 \}$
Input: Candidate pixel $p$ , decision tree classifier $K_p(t)$ , threshold range $[t_{\min}, t_{\max}]$
Output: Corner strength score $V(p)$
low = $t_{\min}$
high = $t_{\max}$
$V(p) = 0$
while low <= high:
    mid = floor((low + high) / 2)
    if $K_p(\text{mid}) == 1$ :
         $V(p) = \text{mid}$
        low = mid + 1
    else:
        high = mid - 1
return $V(p)$
Alternatively, an iterative scheme evaluates the passing pixels on the circle, computes the minimum intensity margin by which they pass the test, increments $t$ by this minimum margin to force a different path through the tree, and repeats until classification fails.

Once $V(p)$ is calculated for all detected corners, non-maximal suppression is applied over a $3 \times 3$ pixel spatial neighborhood: a corner candidate $p$ is retained if and only if $V(p) > V(q)$ for all adjacent neighbor pixels $q$ in the $3 \times 3$ window.
Knowl 4 — 3D Surface Model-Based Repeatability Evaluation Metric
model/method
To evaluate corner detector repeatability under arbitrary 3D camera motion, occlusions, and non-affine surface changes, detected feature locations are mapped across camera views using full 3D surface models of the scene rather than planar homographies.

A detected feature in a source frame is defined as useful if its corresponding 3D scene point reprojects into the visible (non-occluded) field of view of a target frame. A useful feature is defined as repeated if the detector extracts a corner in the target frame within a spatial radius tolerance of $\varepsilon$ pixels (typically $\varepsilon = 5\text{ pixels}$ ) from the true reprojected 3D position.

The overall repeatability $R$ across an image sequence is defined as:

$R = \frac{N_{\text{repeated}}}{N_{\text{useful}}}$

where $N_{\text{repeated}}$ and $N_{\text{useful}}$ represent the total counts of repeated and useful features summed over all directed pairs of frames in the sequence. To compare detectors independently of absolute threshold settings, repeatability $R$ is evaluated as a function of feature density (number of corners extracted per frame, ranging from 0 to 2000 on $640 \times 480$ images). The aggregate quality is summarized by $A$ , the Area Under the Repeatability curve across this range.
Knowl 5 — FAST-ER Generalized Decision Tree Architecture
model/method
FAST-ER (FAST - Enhanced Repeatability) generalizes corner detection by searching over an expanded 48-pixel local neighborhood ( $x \in \{0, 1, \dots, 47\}$ ) within a $7 \times 7$ grid centered at candidate pixel $p$ , rather than restricting tests to a 16-pixel perimeter ring.

The detector is structured as a ternary decision tree where each internal decision node evaluates an offset $x \in \{0, \dots, 47\}$ relative to $p$ and branches into brighter ( $b$ ), similar ( $s$ ), or darker ( $d$ ) subtrees. Each leaf node outputs a boolean classification $K \in \{0, 1\}$ , where 1 represents a corner and 0 represents a non-corner. To enforce monotonicity with respect to threshold variation, any leaf attached to an $s$ branch of its direct parent node is constrained to have $K = 0$ .

To ensure invariance under image rotations, reflections, and intensity inversions without bloating tree depth, the candidate tree is evaluated 16 separate times at runtime across:
- 4 discrete planar rotations ( $0^\circ, 90^\circ, 180^\circ, 270^\circ$ )
- 2 reflection states (original and flipped)
- 2 intensity inversion states (original and inverted)
A pixel $p$ is classified as a corner if and only if any of the 16 transformed applications of the tree evaluates to 1 (logical OR combination). For deployment speed, this 16-way detector is distilled back into a single efficient ternary tree using ID3.
Knowl 6 — FAST-ER Multi-Objective Simulated Annealing Cost Function
equation
To train a ternary decision tree directly for maximal repeatability while preventing trivial over-detection (detecting every pixel) and structural overfitting, the tree configuration is optimized by simulated annealing minimizing the multi-objective cost function $k$ :

$k = \left( 1 + \left( \frac{w_r}{r} \right)^2 \right) \left( 1 + \frac{1}{N} \sum_{i=1}^N \left( \frac{d_i}{w_n} \right)^2 \right) \left( 1 + \left( \frac{s}{w_s} \right)^2 \right)$

where:
- $r \in (0, 1]$ is the sequence repeatability score measured at a fixed threshold $t$ .
- $d_i$ is the number of detected corners in training frame $i$ .
- $N$ is the total number of frames in the training dataset.
- $s$ is the total number of nodes in the decision tree.
- $w_r > 0$ is a weighting constant scaling the penalty for low repeatability ( $w_r = 1$ ).
- $w_n > 0$ is a weighting constant penalizing deviations in target corner density ( $w_n = 3500$ ).
- $w_s > 0$ is a regularizing weight penalizing tree size and complexity ( $w_s = 10000$ ).
Knowl 7 — FAST-ER Tree Optimization via Simulated Annealing
algorithm
FAST-ER decision trees are synthesized by simulated annealing over the discrete tree structure using the multi-objective repeatability cost function $k$ .
Input: Training image sequence, iterations $I_{\max} = 100000$ , parameters $\alpha = 30$ , $\beta = 100$ , threshold $t = 35$ , weights $(w_r, w_n, w_s)$
Output: Optimized decision tree $T$
Initialize $T$ as a random ternary tree of depth 1
Compute initial cost $k = \text{EvaluateCost}(T)$
for $I = 1$ to $I_{\max}$ :
     $T_{\text{cand}} = \text{MutateTree}(T)$
     $k_{\text{cand}} = \text{EvaluateCost}(T_{\text{cand}})$
     $\text{Temperature } \tau = \beta \exp\left( -\alpha \frac{I}{I_{\max}} \right)$
     $\Delta k = k_{\text{cand}} - k$
    if $\Delta k < 0$ or $\text{random}(0, 1) < \exp\left( -\frac{\Delta k}{\tau} \right)$ :
         $T = T_{\text{cand}}$
         $k = k_{\text{cand}}$
return $T$
The mutation function MutateTree selects a node at random and applies one of the following operations:
1. If a leaf node is selected (with equal probability):
  - Replace the leaf with a random depth-1 subtree (a decision node with a random offset in $\{0, \dots, 47\}$ and three leaf children).
  - Flip the leaf label $K \in \{0, 1\}$ (unless the leaf is constrained to 0 on an $s$ branch).
2. If an internal decision node is selected (with equal probability):
  - Replace the test offset with a random offset in $\{0, \dots, 47\}$ .
  - Replace the decision node with a leaf node of random class (subject to branch constraints).
  - Replace one child subtree with an exact copy of another child subtree of that node (enabling merging of redundant branches).
Each candidate tree is compiled into machine code in memory at each step to accelerate cost evaluation across the 16 symmetry transformations. The optimization is repeated across 100 independent restarts.
Knowl 8 — Optimality of 9-Point Arcs in FAST-n Segment Test Detectors
empirical result
Evaluating FAST- $n$ detectors across continuous segment lengths $n \in \{9, 10, 11, 12, 13, 14, 15, 16\}$ shows that $n = 9$ (FAST-9) consistently achieves the highest repeatability across 3D geometric, textural, and non-affine bas-relief test sequences.

For segment lengths $n \le 8$ , the segment test criterion degenerates by responding strongly to 1D straight edges rather than isolated 2D point features. For segment lengths $n > 9$ (including the original FAST-12 heuristic), the criterion is overly strict, failing to detect valid corners under perspective warping and viewpoint changes. Consequently, FAST-9 yields strictly superior repeatability compared to all other FAST- $n$ variants across varying corner densities.

Knowl 9 — Repeatability Comparison Across Feature Detectors

data/table

Corner detector repeatability was evaluated across multiple 3D and planar datasets ('box', 'maze', and 'bas-relief' sets, plus the Oxford planar homography dataset). Detectors were compared using the Area Under the Repeatability curve ( $A$ ) for feature densities ranging from 0 to 2000 detected corners per frame ( $640 \times 480$ resolution) with a spatial matching tolerance of $\varepsilon = 5\text{ pixels}$ .

Detector	$A$ (Area Under Repeatability Curve)
FAST-ER	1313.60
FAST-9	1304.57
Difference of Gaussians (DoG / SIFT)	1275.59
Shi Tomasi	1219.08
Harris	1195.20
Harris-Laplace	1153.13
FAST-12 (Learned)	1121.53
SUSAN	1116.79
Random points baseline	271.73

FAST-ER achieved the highest overall average repeatability score ( $A = 1313.60$ ), outperforming traditional gradient-based and scale-space detectors (DoG, Harris, Shi-Tomasi). FAST-9 achieved the second-highest score ( $A = 1304.57$ ), demonstrating that the 9-point segment test heuristic provides superior geometric stability compared to conventional corner metrics while requiring no spatial derivative computations.

Knowl 10 — Execution Speed and Processing Budget of Feature Detectors

data/table

Computational efficiency and pixel throughput were benchmarked on a 3.0 GHz Intel Pentium 4 processor. Feature detectors were evaluated on monochrome high-definition training fields ( $992 \times 668$ ) and quarter-PAL video test frames ( $352 \times 288$ ). The processing budget represents the percentage of available frame time consumed when processing live $640 \times 480$ video at full frame rate (25 fps / 30 fps) at a feature density of ~500 corners per frame, including non-maximal suppression.

Detector	Training Set		Test Set
	Pixel Rate (MPix/s)	% Budget	Pixel Rate (MPix/s)	% Budget
FAST $n = 9$ (with SSE-2)	188.0	4.90%	179.0	5.15%
FAST $n = 12$ (Learned)	158.0	5.88%	154.0	5.98%
Original FAST ( $n = 12$ )	79.0	11.7%	82.2	11.2%
FAST-ER	75.4	12.2%	67.5	13.7%
SUSAN	12.3	74.7%	13.6	67.9%
Harris (with SSE-2)	8.05	115%	7.90	117%
Shi-Tomasi	6.50	142%	6.50	142%
Difference of Gaussians (DoG)	4.72	195%	5.10	179%

Learned FAST-9 processed 179–188 MPix/s, consuming only ~5% of available frame time. In contrast, standard gradient and scale-space detectors exceeded the 100% budget limit (Harris at 117%, Shi-Tomasi at 142%, DoG at 179–195%), preventing real-time frame-rate operation on single-core desktop architectures.

Coverage note — None was omitted; all key algorithms (FAST tree induction, FAST-ER simulated annealing), mathematical models (segment test, repeatability metric, cost objective), and empirical benchmark datasets/tables were included.

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Citation

MLA

Rosten, E., et al. “Faster and Better: A Machine Learning Approach to Corner Detection”. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 1, 2010, pp. 105–19, https://doi.org/10.1109/TPAMI.2008.275.

APA

Rosten, E., Porter, R., & Drummond, T. (2010). Faster and Better: A Machine Learning Approach to Corner Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(1), 105–119. https://doi.org/10.1109/TPAMI.2008.275

Chicago

Rosten, E., R. Porter, and T. Drummond. 2010. “Faster and Better: A Machine Learning Approach to Corner Detection”. IEEE Transactions on Pattern Analysis and Machine Intelligence 32 (1): 105–19. https://doi.org/10.1109/TPAMI.2008.275.

Harvard

Rosten, E., Porter, R. and Drummond, T. (2010) “Faster and Better: A Machine Learning Approach to Corner Detection”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(1), pp. 105–119. Available at: https://doi.org/10.1109/TPAMI.2008.275.

Vancouver

1. Rosten E, Porter R, Drummond T (2010) Faster and Better: A Machine Learning Approach to Corner Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 32:105–119

BibTeX

@article{Rosten_2010, title={Faster and Better: A Machine Learning Approach to Corner Detection}, volume={32}, ISSN={0162-8828}, url={http://dx.doi.org/10.1109/TPAMI.2008.275}, DOI={10.1109/tpami.2008.275}, number={1}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Rosten, E. and Porter, R. and Drummond, T.}, year={2010}, month=Jan, pages={105–119} }

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Faster and Better: A Machine Learning Approach to Corner Detection

Abstract

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Table of Contents

Knowls

Knowl 1 — Segment Test Criterion for FAST Corner Detection

Knowl 2 — Decision Tree Learning for FAST Corner Detection

Knowl 3 — Corner Response Computation and Non-Maximal Suppression for FAST

Knowl 4 — 3D Surface Model-Based Repeatability Evaluation Metric

Knowl 5 — FAST-ER Generalized Decision Tree Architecture

Knowl 6 — FAST-ER Multi-Objective Simulated Annealing Cost Function

Knowl 7 — FAST-ER Tree Optimization via Simulated Annealing