Evaluation of interest point detectors pdf

We also evaluate the impact of individual algorithm scriptors that are tested. Execution time, a criterion crucial for de- parameters. For this evaluation, a setup to semi-automatically ob- signing real-time systems, receives very little or no attention, and tain stable ground truth for video streams is proposed and explained reported execution times are in the order of seconds to several min- in detail.

In contrast, the evaluation in this work aims at visual tracking in all of the factors mentioned above. Most notably, the perfor- Outline mance measures are chosen with respect to the application of visual tracking and the testbed, which will be detailed in the next section, This report is structured as follows: Section 2 discusses literature consists of video streams with several thousand frames affected by on datasets and existing detector evaluations.

Section 3 reviews noise and motion blur rather than a few high-resolution, low-noise each detector that is included in the evaluation. Section 4 details the still images. Section 5 presents the obtained results, and finally, Section 6 draws conclusions. TR dancy, as pixels do not move independently of each other. Instead, To achieve invariance against changes in scale, the detector a sparse set of features is extracted from the image.

Although work builds a pyramid of images by convoluting the image I with dif- has been done to detect and integrate other features e. In the sim- neighbors [5]. Feature points with low contrast, i. Section 3. Subsequently, 8-neighborhood non-maximum suppres- filter.

For tracking, they suggest using filters that are composed of simple box filters and can therefore be the translation model, where the matrix involved is equivalent to M computed in constant time using the integral image. The computed Eq. Likewise, candidates with c below a certain The approach of detecting local extrema of the image filtered with threshold are rejected. To speed up the computation, one may op- differences of Gaussians DoG was introduced by Lowe [17, 18] tionally increase the sampling intervals, i.

The circle left is the ideal, fully symmetric bi-level approximation of the Laplacian; from left to Figure 1: Filters composed of box filters as used by Fast Hessian right, the approximations are coarser less symmetric , but easier to as approximations to second order derivatives of Gaussians.

Left to compute: octagon, hexagon, box. Figure adapted from Agrawal et al. Weights of black and white [1]. Figure adapted from Bay et al. Agrawal et al. The black point is the current candidate frame j corresponds to point xi in frame i. For general 3D scenes, point p, the 16 grey points are the discretized approximation of the this is very difficult to obtain without a 3D model of the scene.

Figure adapted from Rosten and Drummond Therefore, most existing evaluations [20, 21, 26, 27, 31] use planar [26]. The algorithm operates on a discretized circle around for Hi j may be done by projecting a known pattern onto a static a candidate point p as shown in Fig.

The algorithm was cial markers [9]. However, they occlude a significant part of the further accelerated by training a decision tree to test as few pixels image, rendering it unavailable for the evaluation, require a min- as possible for classifying a candidate pixel as corner or non-corner. In order to apply non-maximum suppres- same from any direction , placed such that their center is in the sion, the following score is computed for each candidate point: plane of the texture.

The markers are 13x The area of the texture itself is 9. The position and size of the balls are manually indicated in [26]. Approximating a Laplacian then yields a torus-shaped using template matching with distance constraints. As this filter is computa- 3. The color model is adapted to the appearance of the balls in tionally rather expensive, three approximations are proposed, each the new frame.

For subsequent frames, a mixture model using getting less symmetric, but easier to compute Fig. For octagons and hexagons, Agrawal et al. Octagons and hexagons can then be de- of freedom x, y, scale between the current and the previous composed in a few trapezoids and thus can also be efficiently com- frame, and the homography between the current image and a puted at any scale.

The speeds are the 1- to 9-folds of 0. Images are shown inverted i. The alignment was substantially im- proved. The transition from one condition to the next is not included 6x 4x 20 frames. Examples of same among the different textures and contain certain amounts of its output are depicted in Fig. As these conditions are exactly the same for 4. In total, the dataset consists of nar textures in 16 different motion patterns each, all recorded with frames.

The The camera movement is reconstructed from the position of the textures are shown in Fig. The motion is mostly smooth, some parts tive order, simulating continuous tracking during smooth motion, exhibit quick movements and motion blur. Execution time is relevant as in in-plane rotation of the object 6x 50 frames. TR Figure 6: Top row: a few examples of the frames in the testbed; bottom row: the same frames, warped to the reference frame. Matching for example fails, as any tion.

This is due to the rotation invariance of its image point can be matched to any other. On the other hand measures. The detector of Heitger combines compu- if the descriptors are spread out, information content is tations in several directions and is not invariant to ro- high and matching is likely to succeed. This is confirmed by Perona who has Information content of the descriptors is measured noticed that the computation in several directions is using entropy.

The more spread out the descriptors are, less stable to an image rotation. ImpHarris and Cottier the higher is the entropy. Section 4. In Section 4. In the case of illumination variations and cam- tion, which characterize local greyvalue patterns. Sec- era noise, ImpHarris and Heitger obtain the best results.

For a viewpoint change ImpHarris shows results which Partitioning of the descriptors is necessary to compute are superior to the other detectors.

The In all cases the results of the improved version of information content criterion of different detectors is the Harris detector are better or equivalent to those of compared in Section 4. For this detector, interest points are largely independent of the imaging conditions; points are geometrically stable.

Entropy Entropy measures the randomness of a variable. The 4. Information Content more random a variable is the bigger the entropy. In the following we are not going to deal with continu- 4. Information Content Criterion ous variables, but with partitions Papoulis, Note that the size To obtain invariance under the group SO 2 2D of the partition influences the results.

If B is a new image rotations , Koenderink Koenderink and van partition formed by subdivisions of the sets of A then Doorn, and Romeny Romeny et al.

Entropy measures average information content. The aver- The average luminance does not characterize the age information content perP message of a set of mes- shape and is therefore not included. In the case of interest points we would like to know how much average information content an interest point 4.

The more distinctive the descriptors are, the larger is the average The computation of entropy requires the partitioning information content. Partitioning is dependent on the distance measure between descriptors. The distance be- 4. Collecting unordered pixel val- The covariance matrix 3 takes into account the vari- ues at an interest point does not represent the shape of ability of the descriptors VE , i.

Collecting ordered pixel noise. This matrix 3 is symmetric positive definite. Its values e. We have therefore chosen to use local rotation a change of reference frame.

We can then define the invariants. Greyvalue derivatives are com- of the coefficients of D. The Mahalanobis distance can puted stably by convolution with Gaussian deriva- then be rewritten as: tives. This is important since the entropy is where L i The probabil- with the Gaussian derivatives G i In this section, we compute the information content of the detectors which are included in our comparison. To obtain a statistically significant measure, a large 5.

Conclusion number of points has to be considered. We use a set of images of different types: aerial images, images In this paper we have introduced two novel evaluation of paintings and images of toy objects. The information criteria: repeatability and information content. These content of a detector is then computed as follows: two criteria present several advantages over existing ones. First of all, they are significant for a large num- 1.

Extract interest points for the set of images. Repeatability compares 2. Compute descriptors cf. Normalize each descriptor cf. The covari- interest point based algorithm which uses two or more ance matrix takes into account the variability of the images of a given scene. Examples are image match- descriptors. Partition the set of normalized descriptors. The cell geometry etc. Information content is relevant for algorithms which 5. Determine the probability of each cell and compute use greyvalue information.

Examples are image match- the entropy with Eq. Furthermore, repeatability as The results are presented in Table 1. It shows that well as information content are independent of human the improved version of Harris produces the highest intervention and apply to real scenes.

The re- The two criteria have been used to evaluate and com- sults obtained for Heitger are almost as good. The two pare several interest point detectors. Repeatability was detectors based on line extraction obtain worse results. This can be explained by their limitation to contour In all cases the improved version of Harris is better than lines which reduces the distinctiveness of their grey- or equivalent to those of the other detectors.

Except for value descriptors and thus their entropy. The results for each image we compute the mean number m of in- information content again show that the improved ver- terest points extracted by the different detectors. We sion of Harris obtains the best results, although the then select m random points over the image using a Heitger detector is a close second.

All of the detec- spatially uniform distribution. Entropy is computed as tors have significantly higher information content than specified above using this random point detector.

The randomly selected points, so they do manage to select result for this detector random is given in Table 1. One random points. The probability to produce a collision possible extension is to adapt these criteria to other low-level features. Another extension would be to de- Table 1. The information content sign an improved interest point detector with respect to for different detectors.

Concerning repeatability, Detector Information content we have seen that detectors show rapid degradation in the presence of scale change. To solve this problem, ImpHarris 6. Another solution might be to estimate the scale Horaud 5.

Concerning in- Cottier 4. In the case of an interest point, the auto- I x xk , yk I y xk , yk I y xk , yk 2 W W correlation function is high for all shift directions. Experimental conditions are using the auto-correlation matrix.

This matrix is de- the same as described in Section 3. The repeatability of the improved version of Harris version is better in both cases. Results are comparable to those Substituting the above approximation 6 into Eq.

Section 3. On the left repeatability rate for an image rotation and on the right the rate for a scale change. On the left the reference image for the rotation sequence. Repeatability rate for the sequence image rotation. Image Rotation Figure 22 shows two images of the rotation sequence.

The repeatability rate for the rotation sequence is dis- played in Fig. Scale Change Figure 25 shows two images of the scale change se- quence. The scale factor between the two images is 4. The repeatability rate for the scale change se- quence is displayed in Fig.

The improved version of Harris and the Cottier detector give the best results as Figure On the left the reference image for the scale change sequence. On the right an image with a scale change of a factor 4. Repeatability rate for the sequence scale change.

Uniform Variation of Illumination Figure 28 shows two images of the uniform variation of illumination sequence, a dark one with a relative grey- value of 0. The repeatability rate for a uniform illumination variation is displayed in Fig. Camera Noise The repeatability rate for camera noise is displayed in Figure Repeatability rate as a function of the localization error Fig. ImpHarris and Heitger give the best results. Uniform variation of illumination sequence.

On the left an image with a relative greyvalue of 0. On the right an image with a relative greyvalue of 1. Repeatability rate for the sequence uniform variation of illumination. Repeatability rate for camera noise sequence. A framework for low level feature extraction.

A fast operator for detection and and Andrew Zisserman for discussions. Harris, C. A combined corner and edge Asada, H. The curvature primal sketch. In Alvey Vision Conference, pp.

A 8 1 :2— Global measures of coherence for edge-detection algorithms. In Proceedings of the Conference on and Machine Intelligence, 19 12 — Kuebler, O. Simulation of neural contour mechanism: From Baker, S. Parametric feature de- simple to end-stopped cells. Vision Research, 32 5 — International Journal of Computer Vision, 27 1 — Heyden, A. Evaluation of corner extraction Beaudet, P.

Rotationally invariant image operators. In Pro- schemes using invariance methods. I, pp. Bowyer, K. 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. This is a preview of subscription content, access via your institution. Rent this article via DeepDyve. Asada, H.

The curvature primal sketch. Google Scholar. Baker, S. Global measures of coherence for edge detector evaluation. Parametric feature detection. International Journal of Computer Vision , 27 1 — Beaudet, P. Rotationally invariant image operators.

Bowyer, K. Edge detector evaluation using empirical ROC curves. Brand, P. Accuracy in image measure. Canny, J. A computational approach to edge detection. Coelho, C. An experimental evaluation of projective invariants. Cooper, J. Early jump-out corner detectors. Cottier, J. Demigny, D. A discrete expression of Canny's criteria for step edge detector performances evaluation.

Deriche, R. Using Canny's criteria to derive a recursively implemented optimal edge detector. International Journal of Computer Vision , 1 2 — Recursively implementing the Gaussian and its derivatives. Recovering and characterizing image features using an efficient model based approach. A computational approach for corner and vertex detection. International Journal of Computer Vision , 10 2 — Dreschler, L. Volumetric model and 3D trajectory of a moving car derived from monocular TV frame sequences of a street scene.

Computer Graphics and Image Processing , — A framework for low level feature extraction. View 1 excerpt, cites background. Interest Points Detection in Color Images. Improved repeatability measures for evaluating performance of feature detectors. The paper deals with content based image retrieval in general and interest point detectors as one of p ossible methods used in object recognition. There are descr ibed current trends in narrowing … Expand.

Abstract In this paper two new criteria are proposed for performance evaluation of point features extracted using SIFT detector. The criteria measure the quality of image features for visual servoing … Expand. In this paper we provide a method for evaluating interest point detectors independently of image descriptors.

This is possible because we have compiled a unique data set enabling us to determine if … Expand. Edge detector evaluation using empirical ROC curves. No PR A method is demonstrated to evaluate edge detector performance using receiver operating characteristic curves.

It involves matching edges to manually specified ground truth to count true positive and … Expand. View 3 excerpts, references methods and background.

Localization properties of direct corner detectors. Journal of Mathematical Imaging and Vision. Gray Level Corner Detection. View 1 excerpt, references background.