Mirror symmetry detection in curves represented by means of the Slope Chain Code

Alvarado-González, Montserrat; Aguilar, Wendy; Garduño, Edgar; Velarde, Carlos; Bribiesca, Ernesto; Médina-Bañuelos, Verónica

doi:10.1016/j.patcog.2018.10.002

Cited by 11 publications

(5 citation statements)

References 14 publications

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“…The ϕ implemented in this work quantifies symmetry degree in quasi‐mirror‐symmetric 2D contours by operations as inversion, concatenation and reflection of the SCC (Alvarado‐Gonzalez et al., 2019).…”

Section: Methodsmentioning

confidence: 99%

“…The invariant descriptors have the advantage that are invariant to scale, rotation and translation since they are based only on the spatial arrangement of pixels contained in the discretized otoliths in the image. We proposed an analysis of sagitta otoliths using the Contact Perimeter ( P c ) and Discrete Compactness ( C d ) as internal discrete descriptors (Bribiesca, 2000); and as external descriptors, the slope chain code (SCC)‐based descriptors such as Discrete Tortuosity ( T d ), Non‐Circularity ( D c ; Bribiesca, 2016), and, Mirror‐Symmetry ( φ ; Alvarado‐Gonzalez et al., 2019). As an additional contribution, we developed a computer tool for otolith shape analysis using these invariant descriptors ( P c , C d , T d , D c , and φ ), as well as other area or perimeter‐based descriptors used in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Invariant morphological descriptors from otolith shape in environment automatic classification

et al. 2021

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One of the ways to recognize patterns is through the intrinsic information of the object's shape by descriptors that allow us to quantitatively describe the contained shape of the object. In ichthyology, the otolith shape recognition is notable for each fish species, which allows the study of the sagitta otolith in species classification, the comparison of otolith shape across the fish ontogeny or growth, and the symmetry analysis of these structures in the case of the same fish. In the last twenty years, there has been a valuable contribution regarding otolith shape analysis and various types of morphometric descriptors have been proposed. The first objective of this work is to propose the implementation of invariant morphometric descriptors, as Discrete Compactness, Discrete Tortuosity, Non-Circularity, and Mirror-Symmetry, and compare their performance with other reported morphometric descriptors. The second objective is the implementation of the Random Forest (RF) algorithm to classify the fish species according their environment (marine, brackish, and freshwater).The right and left sagittae otoliths of 139 marine, brackish, and freshwater species (adults and juveniles) of the Yucatan peninsula and Gulf of Mexico were analysed with invariant and other reported descriptors. The global results show that the invariant descriptors can provide complementary information to other reported descriptors based on area or perimeter, given a low correlation between these features. The environment classification of species using a RF classifier showed that 83% of species correspond positively with their environment classification. This classification analysis can be a useful tool for studies of trophic dynamics, or in archaeological and paleontological studies on fossil fauna this classification tool would allow inferring from remains the environment of the studied communities and their evolution over long periods of time.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Invariant morphological descriptors from otolith shape in environment automatic classification

et al. 2021

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“…Chain codes are another popular method for representing the boundary of geometric objects [36]. The method for detecting the reflection symmetry of open or closed curves represented by the slope chain codes [37] was proposed by Alvarado-Gonzalez et al [38]. The symmetry detection was performed on the level of a chain code symbol sequence, for which the operations of inversion, concatenation, and reflection were used.…”

Section: Local Reflection Symmetrymentioning

confidence: 99%

A Hierarchical Universal Algorithm for Geometric Objects’ Reflection Symmetry Detection

et al. 2022

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A new algorithm is presented for detecting the global reflection symmetry of geometric objects. The algorithm works for 2D and 3D objects which may be open or closed and may or may not contain holes. The algorithm accepts a point cloud obtained by sampling the object’s surface at the input. The points are inserted into a uniform grid and so-called boundary cells are identified. The centroid of the boundary cells is determined, and a testing symmetry axis/plane is set through it. In this way, the boundary cells are split into two parts and they are faced with the symmetry estimation function. If the function estimates the symmetric case, the boundary cells are further split until a given threshold is reached or a non-symmetric result is obtained. The new testing axis/plane is then derived and tested by rotation around the centroid. This paper introduces three techniques to accelerate the computation. Competitive results were obtained when the algorithm was compared against the state of the art.

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“…The definition and measurement of tortuosity has been extensively studied on medical 13,14 and other forms of images in the literature. 15,16 A number of measures have been defined with respect to different criteria, such as the length-based, [17][18][19] the angle-based, 12,13,15,20 and the curvature-based measures. 14,21 It is worth noting that most of these existing measures are designed for quantifying specific anatomical structures (such as retinal vessel, 17 intracerebral vasculature, 18 and corneal nerve 22 ).…”

Section: Introductionmentioning

confidence: 99%

“…Once the corneal nerves are traced in IVCM images, each nerve fiber can be represented as pixels which form a curvilinear structure and its tortuosity can then be measured. The definition and measurement of tortuosity has been extensively studied on medical 13,14 and other forms of images in the literature 15,16 . A number of measures have been defined with respect to different criteria, such as the length‐based, 17–19 the angle‐based, 12,13,15,20 and the curvature‐based measures 14,21 .…”

Section: Introductionmentioning

confidence: 99%

Corneal nerve tortuosity grading via ordered weighted averaging‐based feature extraction

Chen

Xie

et al. 2020

Medical Physics

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Purpose: Tortuosity of corneal nerve fibers acquired by in vivo Confocal Microscopy (IVCM) are closely correlated to numerous diseases. While tortuosity assessment has conventionally been conducted through labor-intensive manual evaluation, this warrants an automated and objective tortuosity assessment of curvilinear structures. This paper proposes a method that extracts the image-level features for corneal nerve tortuosity grading. Methods: For an IVCM image, all corneal nerve fibers are first segmented and then, their tortuosity are calculated by morphological measures. The ordered weighted averaging (OWA) approach, and the k-Nearest-Neighbor guided dependent ordered weighted averaging (kNNDOWA) approach are proposed to aggregate the tortuosity values and form a set of extracted features. This is followed by running the Wrapper method, a supervised feature selection, with an aim to identify the most informative attributes for tortuosity grading. Results: Validated on a public and an in-house benchmark data sets, experimental results demonstrate superiority of the proposed method over the conventional averaging and length-weighted averaging methods with performance gain in accuracy (15.44% and 14.34%, respectively). Conclusions: The simultaneous use of multiple aggregation operators could extract the image-level features that lead to more stable and robust results compared with that using average and lengthweighted average. The OWA method could facilitate the explanation of derived aggregation behavior through stress functions. The kNNDOWA method could mitigate the effects of outliers in the imagelevel feature extraction.

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Mirror symmetry detection in curves represented by means of the Slope Chain Code

Cited by 11 publications

References 14 publications

Invariant morphological descriptors from otolith shape in environment automatic classification

Invariant morphological descriptors from otolith shape in environment automatic classification

A Hierarchical Universal Algorithm for Geometric Objects’ Reflection Symmetry Detection

Corneal nerve tortuosity grading via ordered weighted averaging‐based feature extraction

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