The Expression and Comparison of Healthy and Ptotic Upper Eyelid Contours Using a Polynomial Mathematical Function

Mocan, Mehmet Cem; İlhan, Hacer; Gürçay, Haşmet; Dikmetaş, Özlem; Karabulut, Erdem; Erdener, Uğur; İrkeç, Murat

doi:10.3109/02713683.2013.860992

Cited by 21 publications

(21 citation statements)

References 14 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…; Mocan et al. ). The approaches to image analysis in these previous studies, however, are not integrative and therefore yield results that are partial and fragmentary.…”

Section: Discussionmentioning

confidence: 97%

“…intra‐class correlation coefficients (ICCs) are large when there is little variation within the measurements of observers (Mocan et al. ).…”

Section: Methodsmentioning

confidence: 99%

“…; Mocan et al. ). However, most of these studies report virtual measurements instead of actual measurements, assuming arbitrary corneal diameters such as reference pixel widths (Cruz et al.…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Topographic analysis of eyelid position using digital image processing software

Chun

Park

et al. 2017

Acta Ophthalmologica

View full text Add to dashboard Cite

show abstract

“…; Mocan et al. ). The approaches to image analysis in these previous studies, however, are not integrative and therefore yield results that are partial and fragmentary.…”

Section: Discussionmentioning

confidence: 97%

“…intra‐class correlation coefficients (ICCs) are large when there is little variation within the measurements of observers (Mocan et al. ).…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Topographic analysis of eyelid position using digital image processing software

Chun

Park

et al. 2017

Acta Ophthalmologica

View full text Add to dashboard Cite

show abstract

“…Eyelid contour analyses have been performed with various methods, including mathematical polynomial functions, image processing, and mathematic software. Mocan et al extracted eyelid contours using third-degree equations of polynomial functions [ 6 ]. Cruz et al, Akaishi et al, and Şendül et al used T/N distances and area ratios [ 4 , 5 , 8 ], while Ahn et al and Ribeiro et al drew 12 oblique lines from the corneal reflex to the upper lid margin [ 7 , 14 ] and Danesh et al determined 10 reference points on the upper lid margin to compare the symmetry of the upper lid [ 3 ].…”

Section: Discussionmentioning

confidence: 99%

Comparing the symmetry of upper eyelid following unilateral ptosis correction

Aytoğan

Ayıntap

2021

BMC Ophthalmol

View full text Add to dashboard Cite

Background Margin Reflex Distance 1(MRD 1) only describes the central height of upper eyelid and relies on the examiner’s experience and disregards eyelid contour abnormalities. Therefore MRD 1 may not be sufficient for an acceptable result to evaluate the outcomes of ptosis surgery. The primary purpose of this study was to assess outcomes of unilateral ptosis correction based on parameters including degree of symmetry, MRD 1, peak height of the upper lid, temporal and nasal ocular surface area, and temporal/nasal area ratio with an objective, quantitative, and repeatable method. Methods This study was designed as a retrospective non-randomized case-control study. Medical records of the patients with unilateral ptosis between October 2015 and December 2020 were reviewed. Patients with unilateral ptosis who underwent surgical correction and levator function of 5 mm or greater were included in the study. Two groups were defined; ptotic eye was case group and contralateral eye was control group. Data analysis was performed Image J and Matlab softwares. Results Thirty-four patients were included in the study. Mean age of patients was 58.8 ± 12.7 years (range 15–75 years). Mean follow-up time was 19.5 ± 7.3 months (range 8–40 months). Four patients were diagnosed with congenital ptosis and 30 patients aponeurotic ptosis. Mean preoperative degree of symmetry for overall eyelid contour was 36.6 ± 27.5% (range 1–92%). Mean postoperative degree of symmetry for overall eyelid contour was 72.4 ± 16.5% (range 55–92%). Temporal/Nasal (T/N) area ratios for contralateral normal eye was 1.19 pre-postoperative, and it was 1.11 preoperatively, 1.15 postoperatively for operated ptotic eye. Conclusions This study primarily demonstrated a quantitative, objective, and repeatable method to investigate the degree of symmetry after eyelid surgeries. Secondly, this study suggested that T/N ratio may not be a reliable parameter to evaluate the eyelid symmetry.

show abstract

“…Within the periocular region, geometric models have been utilized to better understand the relationship between the three-dimensional nature of the eyelid and eyebrow. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 The authors describe a mathematical model for analyzing eyebrow curvature that can be applied broadly to curvilinear facial features. This method provides a simple and reliable tool that can help facilitate the analysis of standardized images.…”

mentioning

confidence: 99%

Mathematical Modeling of Eyebrow Curvature

et al. 2022

View full text Add to dashboard Cite

The aim of the study is to describe a mathematical model for analyzing eyebrow curvature that can be applied broadly to curvilinear facial features. A total of 100 digital images (50 men, 50 women) were obtained from standardized headshots of medical professionals. Images were analyzed in ImageJ by plotting either 8 or 15 points along the inferior-most row of contiguous brow cilia. A best-fit curve was automatically fit to these points in Microsoft Excel. The second derivative of the second-degree polynomial and a fourth-degree polynomial were used to evaluate brow curvature. Both techniques were subsequently compared with each other. A second-degree polynomial and fourth-degree polynomial were fit to all eyebrows. Plotting 15 points yielded greater goodness-of-fit than plotting 8 points along the inferior brow and allowed for more sensitive measurement of curvature across all images. A fourth-degree polynomial function provided a closer fit to the eyebrow than a second-degree polynomial function. This method provides a simple and reliable tool for quantitative analysis of eyebrow curvature from images. Fifteen-point plots and a fourth-degree polynomial curve provide a greater goodness-of-fit. The authors believe the described technique can be applied to other curvilinear facial features and will facilitate the analysis of standardized images.

show abstract

The Expression and Comparison of Healthy and Ptotic Upper Eyelid Contours Using a Polynomial Mathematical Function

Abstract: The healthy and abnormal eyelid contour can be defined and differentiated using a polynomial mathematical function.

Cited by 21 publications

References 14 publications

Topographic analysis of eyelid position using digital image processing software

Topographic analysis of eyelid position using digital image processing software

Comparing the symmetry of upper eyelid following unilateral ptosis correction

Mathematical Modeling of Eyebrow Curvature

Contact Info

Product

Resources

About