# Shape recognition with edge-based features

## Summary (2 min read)

### 1 Introduction

- They obtain excellent results for objects which are locally planar and have a distinctive texture [21].
- The authors goal is to recognize classes of roughly planar objects of wiry components against a cluttered background.
- A very important property of their recognition approach is scale invariance [12, 14].
- A second problem area is occlusions and background clutter.
- These can significantly change the appearance of features localized on object boundaries.

### 1.1 Background

- The authors approach builds on recent object recognition methods.
- In the context of scale invariant features Mikolajczyk and Schmid [14] developed a scale invariant interest point detector.
- Therefore, many authors also use geometric relations between features to correctly resolve ambiguous matches.
- The latter successfully detect objects with wiry components in cluttered backgrounds.
- Other related approaches using edge information are those of Belongie et al. [3] who use 2D shape signatures based on edges in the context of shape matching, although scale invariance and background clutter problems are not addressed in their work, and the projectively invariant shape descriptor used by Sullivan and Carlsson [25].

### 1.2 Overview

- Section 2 presents the new feature detector and local edge descriptor.
- Section 3 describes the two stages of the recognition system: first clustering on a local transformation to reduce ambiguity, and then estimating a global transformation to detect the object in an image.
- In more detail, the authors combine an appearance distance between feature descriptors and local geometric consistency to compute the scores for point matches.
- The best matches with relatively few outliers are then used to vote in the Hough space of local affine transformations.
- The distinctive clusters in this space are used to detect and localize the objects.

### 2 Local features

- In the following the authors describe their feature detector.
- The authors objective is to determine the edge neighbourhood that is related to the scale of the object.
- The authors then show how they deal with occlusions and background clutter.
- Finally the authors present the descriptor that represents the edge shape in the point neighbourhood.

### 2.1 Support regions

- In their task edges of low curvature and their spatial relations are very characteristic of the object.
- It is well know that edge features are present at various scales and can change their appearance at different scales.
- Given a point the authors compute the Laplacian responses for several scales.
- There are several advantages to this approach.
- To reduce the background influence, the point neighbourhood is divided into two parts separated by a chain of dominant edges, and descriptors are computed separately for each part as described below.

### 2.2 Edge Descriptors

- A descriptor that captures the shape of the edges and is robust to small geometric and photometric transformations is needed for this approach.
- A comparative evaluation of descriptors in [16] showed that SIFT descriptors [12] perform significantly better than many other local descriptors recently proposed in the literature.
- For each region part (cf. figure (a)) the authors build a 3D histogram of gradient values, for which the dimensions are the edge point coordinates (x, y) and the gradient orientation.
- The descriptor is built from two histograms.
- The descriptor of each region part contains also the points on the dominant edge.

### 3 Coarse-to-fine geometric consistency

- The recognition strategy consists of two main stages aimed at establishing matches between the model and target image.
- The second stage is clustering the pose of the whole object in a coarsely partitioned affine space.
- This geometric consistency is used to weight the descriptor distance of every neighbouring point pair.
- The matched points xa xb give a hypothesis of the local similarity transformation between the images, where the scale change is σa b σa σb and the rotation is φa b φa φb (cf. figure 6).
- The votes in the transformation space are weighted by the scores obtained in the previous stage.

### 4 Results

- To validate their approach the authors detect bicycles in cluttered outdoor scenes under wide viewpoint changes.
- Other clusters in the space are insignificant.
- Figures 7(e) and (f) present examples of multiple objects of different scales and small changes of aspect ratio.
- The local edge descriptors convey information about the shape of the edges and not about their exact appearance in the image.
- The authors can learn, for example, the variation of the descriptor computed on the same parts of similar objects.

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##### Citations

46,906 citations

### Cites background from "Shape recognition with edge-based f..."

...Mikolajczyk et al. (2003) have developed a new descriptor that uses local edges while ignoring unrelated nearby edges, providing the ability to find stable features even near the boundaries of narrow shapes superimposed on background clutter....

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14,708 citations

4,107 citations

### Cites background or methods from "Shape recognition with edge-based f..."

...An additional post-processing method can be used to separate the foreground from the background (Borenstein and Ullman, 2002; Mikolajczyk and Schmid, 2003b)....

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...The accuracy of the feature localization and shape is critical for local descriptors, for example, differential descriptors fail if this error is significant (Mikolajczyk and Schmid, 2003a)....

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...The reader is referred to Mikolajczyk and Schmid (2003a), for a detailed evaluation of different descriptors computed on scale and affine invariant regions....

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...The evaluation of interest point detectors presented in Schmid et al. (2000) demonstrate an excellent performance of the Harris detector compared to other existing approaches (Cottier, 1994; Forstner, 1994; Heitger et al....

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...This can be achieved by using (i) more distinctive descriptors (see Mikolajczyk and Schmid, 2003a for a performance evaluation of different descriptors computed for affine-invariant regions) or (ii) semi-local ge- ometric consistency (Dufournaud et al., 2000; Pritchett and Zisserman, 1998; Tell and…...

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3,359 citations

### Cites background from "Shape recognition with edge-based f..."

...…regions which are covariant only to similarity transformations (i.e., in particular scale), such as (Lowe, 1999, 2004; Mikolajczyk and Schmid, 2001; Mikolajczyk et al., 2003), or other methods of computing affine invariant descriptors, such as image lines connecting interest points (Matas et al.,…...

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..., in particular scale), such as (Lowe, 1999, 2004; Mikolajczyk and Schmid, 2001; Mikolajczyk et al., 2003), or other methods of computing affine invariant descriptors, such as image lines connecting interest points (Matas et al....

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1,144 citations

##### References

28,073 citations

### "Shape recognition with edge-based f..." refers methods in this paper

...To find the local features we first extract edges with a multi-scale Canny edge detector [6] using Gaussian derivatives at several pre-selected scales, with the scale interval of 1....

[...]

16,989 citations

### "Shape recognition with edge-based f..." refers background or methods in this paper

...Several authors use the Laplacian operator for this purpose [11, 12, 14, 20]....

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...The widely used Harris [9] and DoG [12] detectors are not suitable for our purpose as the first one detects corner-like structures and the second one mostly blobs....

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...Third, the descriptor generalizes Lowe’s SIFT method [12] to edges....

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...A very important property of our recognition approach is scale invariance [12, 14]....

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...Numerous recent approaches to object recognition [2, 12, 13, 14, 15, 20, 24] represent the object by a set of colour or grey-level textured local patches....

[...]

13,993 citations

### "Shape recognition with edge-based f..." refers methods in this paper

...The widely used Harris [9] and DoG [12] detectors are not suitable for our purpose as the first one detects corner-like structures and the second one mostly blobs....

[...]

7,057 citations

### "Shape recognition with edge-based f..." refers background in this paper

...A comparative evaluation of descriptors in [16] showed that SIFT descriptors [12] perform significantly better than...

[...]

6,693 citations

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##### Frequently Asked Questions (10)

###### Q2. What is the key property of the scale invariance approach?

The scale invariance can locally approximate affine deformations, thereby additionally providing some immunity to out of plane rotations for planar objects.

###### Q3. Why do strong edges often appear on the boundaries?

Since strong edges often appear on the boundaries they can be used to split the support regions before computing the descriptors.

###### Q4. What was the first successful method in the early nineties?

Edge based method with affine [10] or projective [19] invariance, were successful in the early nineties, but fell out of favour partly because of the difficulties of correctly segmenting long edge curves.

###### Q5. What is the need for a descriptor that captures the shape of the edges?

A descriptor that captures the shape of the edges and is robust to small geometric and photometric transformations is needed for this approach.

###### Q6. Why do the authors use 1 dE to avoid zero in the denominator?

The authors use 1 dE to avoid zero in the denominator (cf. equation 1), which can happen when the distance between descriptor vectors equals zero.

###### Q7. What is the first stage of the recognition strategy?

The first stage is filtering matches by taking into account the similarity of their histogram descriptors and the local geometric consistency of a similarity transformations between spatially neighbouring matches.

###### Q8. What is the recent development of affine invariant features?

many authors developed affine invariant features based on the second moment matrix [2, 15, 20] or other methods [13, 24].

###### Q9. What is the score for a given pair of points?

The matching score for a given pair of points is:v xa xb 11 dE xa xb ∑i j βi jαi j1 dE xi x j (1)where α and β are the penalizing functions defined byαi j 1 1 0 1 φa b φi j βi j σa b σi j i f σa b σi j 1σi j σa b otherwise Points xi x j are spatial neighbours of points xa xb (cf. figure 6) within a distance 5σa 5σb respectively.

###### Q10. What is the scale parameter for which the Laplacian attains an extremum?

For a perfect step-edge the scale parameter for which the Laplacian attains an extremum is in fact equal to the distance to the step-edge.