Representation of signals by local symmetry decomposition

Gnutti, Alessandro; Guerrini, Fabrizio; Leonardi, Riccardo

doi:10.1109/eusipco.2015.7362530

Cited by 14 publications

(18 citation statements)

References 8 publications

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“…of the convolution support computed for a given symmetry center. This process may at first look similar to the one in [12]. However, in that work the search for local symmetry still took inspiration from a reasoning similar to that conveyed by Eq.…”

Section: Correlation For Symmetry Detection In 1-d Signalsmentioning

confidence: 99%

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A normalized mirrored correlation measure for data symmetry detection

Gnutti

Guerrini

Leonardi

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Symmetry detection algorithms are enjoying a renovated interest in the scientific community, fueled by recent advancements in computer vision and computer graphics applications. This paper is inspired by recent efforts in building a symmetric object detection system in natural images. In particular, it is first shown how correlation can be a core operator that allows finding local reflection symmetry points in 1-D sequences that are optimal in an energetic sense. Then, the importance of 2-D correlation in natural images to correctly align the symmetric object axis is demonstrated. Using the correlation as described is crucial in boosting the performance of the system, as proven by the results on a standard dataset.

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Section: Correlation For Symmetry Detection In 1-d Signalsmentioning

confidence: 99%

“…The extent of the window is of course an important parameter that may be adjusted as needed using a procedure similar to that adopted in [12]. However, to keep the discussion simple, for the rest of the paper fixed-length windows covering n p = 100 locations around each extreme point are employed.…”

Section: Correlation For Symmetry Detection In 1-d Signalsmentioning

confidence: 99%

A normalized mirrored correlation measure for data symmetry detection

Gnutti

Guerrini

Leonardi

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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“…The product with √ has the same effect as in Eq. (6). The feature 2 is also normalized image-wise in the [0, 1] interval by dividing its value by the maximum found for each image.…”

Section: Candidate Symmetry Axesmentioning

confidence: 99%

“…So, we start with a basic mathematic tool that was proposed in [6] to find hierarchies of symmetries in the raw data for the 1D domain. In that work, detecting whether a 1D digital sequence possesses reflective symmetry is a problem that is solved by decomposing the sequence into its even and odd constitutive parts and then by analyzing their respective energy.…”

Section: Introductionmentioning

confidence: 99%

On Reflection Symmetry In Natural Images

Gnutti

Guerrini

Leonardi

2017

Proceedings of the 15th International Workshop on Content-Based Multimedia Indexing

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Many new symmetry detection algorithms have been recently developed, thanks to an interest revival on computational symmetry for computer graphics and computer vision applications. Notably, in 2013 the IEEE CVPR Conference organized a dedicated workshop and an accompanying symmetry detection competition. In this paper we propose an approach for symmetric object detection that is based both on the computation of a symmetry measure for each pixel and on saliency. The symmetry value is obtained as the energy balance of the even-odd decomposition of a patch w.r.t. each possible axis. The candidate symmetry axes are then identified through the localization of peaks along the direction perpendicular to each considered axis orientation. These found candidate axes are finally evaluated through a confidence measure that also allow removing redundant detected symmetries. The obtained results within the framework adopted in the aforementioned competition show significant performance improvement.

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“…In the same section, we will give more examples of potential applications, for 140 example the one presented in [6], before we draw the conclusions in Section 7.…”

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confidence: 99%

Even/odd decomposition made sparse: A fingerprint to hidden patterns

2017

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The very fundamental operation of even/odd decomposition is at the core of some of the simplest information representation and signal processing tasks. So far most of its use has been for rearranging data to provide fast implementations of various types of transforms (Fourier, DCT, ...) or for achieving elementary data transformation, such as the Walsh-Hadamard transforms. This work proposes to look into the decomposition framework to obtain a richer perspective. In the context of an iterated even/odd decomposition, it is possible to pinpoint intermediate layered levels of symmetries which cannot be easily captured in the original data. In addition this determines a hierarchical fingerprinting for any sort of continuous finite support analog signal or for any discrete-time sequence which may turn out useful in several recognition or categorization tasks. It also may help to achieve sparsity within a natural hierarchical framework, which could be easily extented for many other types of orthogonal transformations. This paper also suggests a global measure of the energy imbalance across the hierarchy of the decomposition to capture the overall fingerprinting of this interpretation . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 It also may help to achieve sparsity within a natural hierarchical framework, which could be easily extented for many other types of orthogonal transformations. This paper also suggests a global measure of the energy imbalance across the hierarchy of the decomposition to capture the overall fingerprinting of this interpretation.

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Representation of signals by local symmetry decomposition

Cited by 14 publications

References 8 publications

A normalized mirrored correlation measure for data symmetry detection

A normalized mirrored correlation measure for data symmetry detection

On Reflection Symmetry In Natural Images

Even/odd decomposition made sparse: A fingerprint to hidden patterns

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