The size of the shadow boundary projection

1998 ◽  
Vol 95 (1) ◽  
pp. 519-527
Author(s):  
Andreas Knauf
Keyword(s):  
Shadow Boundary ◽  
Boundary Projection

The size of the shadow boundary projection

1998 ◽  
Vol 95 (4) ◽  
pp. 519-527
Author(s):  
Andreas Knauf
Keyword(s):  
Shadow Boundary ◽  
Boundary Projection

Incremental Length Diffraction Coefficients for the Shadow Boundary of a General Cylinder

1997 ◽  
Author(s):  
Thorkild B. Hansen ◽  
Robert A. Shore
Keyword(s):  
Shadow Boundary ◽  
Diffraction Coefficients

An immersed boundary projection method for simulating the inextensible vesicle dynamics

2020 ◽  
Vol 408 ◽  
pp. 109277
Author(s):  
Kian Chuan Ong ◽  
Ming-Chih Lai
Keyword(s):  
Projection Method ◽  
Immersed Boundary ◽  
Vesicle Dynamics ◽  
Boundary Projection

Creeping‐wave theory applied to impulse propagation around a meteorological shadow boundary

1990 ◽  
Vol 88 (1) ◽  
pp. 462-468
Author(s):  
A. J. Cramond ◽  
C. G. Don
Keyword(s):  
Wave Theory ◽  
Shadow Boundary ◽  
Impulse Propagation ◽  
Creeping Wave

scholarly journals Use of Gradient-Based Shadow Detection for Estimating Environmental Illumination Distribution

2018 ◽  
Vol 8 (11) ◽  
pp. 2255 ◽  
Author(s):  
Sangyoon Lee ◽  
Hyunki Hong
Keyword(s):  
Three Dimensional ◽  
Local Features ◽  
Shadow Detection ◽  
Reference Object ◽  
Light Sources ◽  
Illumination Estimation ◽  
Shadow Boundary ◽  
Sampling Position ◽  
Gradient Based ◽  
Edge Based

Environmental illumination information is necessary to achieve a consistent integration of virtual objects in a given image. In this paper, we present a gradient-based shadow detection method for estimating the environmental illumination distribution of a given scene, in which a three-dimensional (3-D) augmented reality (AR) marker, a cubic reference object of a known size, is employed. The geometric elements (the corners and sides) of the AR marker constitute the candidate’s shadow boundary; they are obtained on a flat surface according to the relationship between the camera and the candidate’s light sources. We can then extract the shadow regions by collecting the local features that support the candidate’s shadow boundary in the image. To further verify the shadows passed by the local features-based matching, we examine whether significant brightness changes occurred in the intersection region between the shadows. Our proposed method can reduce the unwanted effects caused by the threshold values during edge-based shadow detection, as well as those caused by the sampling position during point-based illumination estimation.

Frequency Characteristics of Diffracted Waves Considering Transition Region of GTD Shadow Boundary

2011 ◽  
Author(s):  
Jiro Iwashige ◽  
Leonard Barolli ◽  
Katsuki Hayashi ◽  
Ryo Nagao ◽  
Yuki Isayama
Keyword(s):  
Transition Region ◽  
Frequency Characteristics ◽  
Shadow Boundary ◽  
Diffracted Waves

scholarly journals Characterizations of central symmetry for convex bodies in Minkowski spaces

2009 ◽  
Vol 46 (4) ◽  
pp. 493-514
Author(s):  
Gennadiy Averkov ◽  
Endre Makai ◽  
Horst Martini
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Analogous Result ◽  
Area Measure ◽  
Minkowski Metric ◽  
Surface Area Measure ◽  
Shadow Boundary ◽  
Dimensional Minkowski Space ◽  
Centrally Symmetric ◽  
Definition Of

K. Zindler [47] and P. C. Hammer and T. J. Smith [19] showed the following: Let K be a convex body in the Euclidean plane such that any two boundary points p and q of K , that divide the circumference of K into two arcs of equal length, are antipodal. Then K is centrally symmetric. [19] announced the analogous result for any Minkowski plane \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{M}^2$$ \end{document}, with arc length measured in the respective Minkowski metric. This was recently proved by Y. D. Chai — Y. I. Kim [7] and G. Averkov [4]. On the other hand, for Euclidean d -space ℝ d , R. Schneider [38] proved that if K ⊂ ℝ d is a convex body, such that each shadow boundary of K with respect to parallel illumination halves the Euclidean surface area of K (for the definition of “halving” see in the paper), then K is centrally symmetric. (This implies the result from [19] for ℝ 2 .) We give a common generalization of the results of Schneider [38] and Averkov [4]. Namely, let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{M}^d$$ \end{document} be a d -dimensional Minkowski space, and K ⊂ \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{M}^d$$ \end{document} be a convex body. If some Minkowskian surface area (e.g., Busemann’s or Holmes-Thompson’s) of K is halved by each shadow boundary of K with respect to parallel illumination, then K is centrally symmetric. Actually, we use little from the definition of Minkowskian surface area(s). We may measure “surface area” via any even Borel function ϕ: Sd −1 → ℝ, for a convex body K with Euclidean surface area measure dSK ( u ), with ϕ( u ) being dSK ( u )-almost everywhere non-0, by the formula B ↦ ∫ B ϕ( u ) dSK ( u ) (supposing that ϕ is integrable with respect to dSK ( u )), for B ⊂ Sd −1 a Borel set, rather than the Euclidean surface area measure B ↦ ∫ BdSK ( u ). The conclusion remains the same, even if we suppose surface area halving only for parallel illumination from almost all directions. Moreover, replacing the surface are a measure dSK ( u ) by the k -th area measure of K ( k with 1 ≦ k ≦ d − 2 an integer), the analogous result holds. We follow rather closely the proof for ℝ d , which is due to Schneider [38].

Sign in / Sign up

Export Citation Format

Share Document