Reflection symmetry detection of shapes based on shape signatures

Nguyễn, Thanh Phương; Truong, Hung Phuoc; Nguyen, Thanh Tuan; Kim, Yong-Guk

doi:10.1016/j.patcog.2022.108667

Cited by 9 publications

(5 citation statements)

References 27 publications

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“…When this angle is θ, the corresponding ρ i.e. ρ is given by ρ = x c cos θ + y c sin θ, which means that (x c , y c ) verifies the equation of the line ρ = x cos θ + y sin θ (22) Consequently, derivating the SSRT with respect to θ and ρ provides, in the image domain, a line of which equation is represented by (22). Now, before showing the relationship between the orientation φ in (3) and the angle θ in (21), and to be in accordance with our proposition which states that the SSRT maximum defines the inertia principal axis, we must prove that the computed critical point ( θ, ρ) is a maximum.…”

Section: The Scale Space Radon Transform Maximum and The Main Inertia...mentioning

confidence: 89%

“…It results that if a point of coordinates (x, y) is rotated by π around O(0, 0) then, its new coordinates are Looking at the SSRT Šf of centrally symmetric objects centred in f in Fig. 4, we can notice the presence of reflection symmetry, which definition can be found in [22], over the axe ρ = 0 in the SSRT sinograms. This symmetry is the result of the reflection symmetry of the SSRT projections, Šf θ (ρ), as seen in the same figure.…”

Section: Example Of Application : Measuring Central Symmetry Of Binar...mentioning

confidence: 95%

“…It results that using one reflectionnaly symmetric projection to construct f guarantees the central symmetry of the latter, but does not guarantee, unfortunately, the central symmetry of f . Indeed, if this projection of which orientation, says γ, corresponds to the orientation of an existing reflection symmetry in f , which also produces a reflection symmetry in the projection Řf γ , as seen in [22] and subsequently in Šf γ (ρ), Input: Binary image f , the scale σ sym , threshold ǫ, ρ and θ steps Output: Sym 1 Compute σ, Řf , g(σ), Šf with ( 2) and ( θ, ρ) = argmax then, f will be centrally symmetric even if f has only one reflection symmetry. To avoid this situation, we propose to sample the SSRT space into three equispaced projections, Šf θ , Šf θ+π/3 and Šf θ+2π/3 .…”

Section: Sampling the Projections For Central Symmetry Measurementmentioning

confidence: 99%

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Scale space radon transform-based inertia axis and object central symmetry estimation

Goumeidane¹,

Ziou²,

Nacereddine³

2023

Preprint

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Inertia Axes are involved in many techniques for image content measurement when involving information obtained from lines, angles, centroids... etc. We investigate, here, the estimation of the main axis of inertia of an object in the image. We identify the coincidence conditions of the Scale Space Radon Transform (SSRT) maximum and the inertia main axis. We show, that by choosing the appropriate scale parameter, it is possible to match the SSRT maximum and the main axis of inertia location and orientation of the embedded object in the image. Furthermore, an example of use case is presented where binary objects central symmetry computation is derived by means of SSRT projections and the axis of inertia orientation. To this end, some SSRT characteristics have been highlighted and exploited. The experimentations show the SSRT-based main axis of inertia computation effectiveness. Concerning the central symmetry, results are very satisfying as experimentations carried out on randomly created images dataset and existing datasets have permitted to divide successfully these images bases into centrally symmetric and non-centrally symmetric objects.

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Section: The Scale Space Radon Transform Maximum and The Main Inertia...mentioning

confidence: 89%

Section: Example Of Application : Measuring Central Symmetry Of Binar...mentioning

confidence: 95%

Section: Sampling the Projections For Central Symmetry Measurementmentioning

confidence: 99%

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Scale space radon transform-based inertia axis and object central symmetry estimation

Goumeidane¹,

Ziou²,

Nacereddine³

2023

Preprint

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“…Для оценки меры симметрии используется критерий χ-квадрат соответствия отражённой проекции исходной. В последующей работе [15] было показано, что использование данной оценки в качестве критерия симметричности имеет теоретическое обоснование. Хотя такой метод способен очень быстро обрабатывать входные изображения с фигурами, близкими к идеально симметричным, находя для них «правильную» ось симметрии, результаты для недостаточно симметричных фигур (например, симметричных фигур с исключенной или добавленной частью) часто оказываются далеки от ожидаемых.…”

Section: обзор существующих методовunclassified

“…Также предложенный метод сравнивался с методом Нгуена [15], который использует другую меру симметрии -коэффициент корреляции между проекцией фигуры на прямую и её отражением:…”

Section: экспериментыunclassified

Detection of the Optimal Reflection Symmetry Axis with the Jaccard Index by Projection-based Method

Lomov

Seredin

Kushnir

et al. 2022

Proceedings of the 32nd International Conference on Computer Graphics and Vision

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This study determines the optimal reflection symmetry axis of an object in a binary image using the Jaccard index. We propose to find the global optimum on the grid by estimating the upper bounds of the Jaccard index with the Radon transform. Several approaches to improving the Jaccard index computation for a given line are considered. Some strategies for enumerating possible symmetry axes and selecting the initial approximation are proposed. The experiments show that the Jaccard index for the optimal axis found by the proposed method is not inferior to the exhaustive bruteforce of the axes passing through the points of the object contour considering the rasterization error. In terms of speed, the proposed method significantly exceeds the previously developed methods for limiting the exhaustive search.

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