Statistical Approach to Shape from Shading: Reconstruction of Three-Dimensional Face Surfaces from Single Two-Dimensional Images

1996 ◽  
Vol 8 (6) ◽  
pp. 1321-1340 ◽  
Author(s):  
Joseph J. Atick ◽  
Paul A. Griffin ◽  
A. Norman Redlich
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Practical Interest ◽  
Principal Component ◽  
Shape From Shading ◽  
Shape Space ◽  
Two Dimensional ◽  
Two Dimensional Image ◽  
Low Dimensional ◽  
Dimensional Object

The human visual system is proficient in perceiving three-dimensional shape from the shading patterns in a two-dimensional image. How it does this is not well understood and continues to be a question of fundamental and practical interest. In this paper we present a new quantitative approach to shape-from-shading that may provide some answers. We suggest that the brain, through evolution or prior experience, has discovered that objects can be classified into lower-dimensional object-classes as to their shape. Extraction of shape from shading is then equivalent to the much simpler problem of parameter estimation in a low-dimensional space. We carry out this proposal for an important class of three-dimensional (3D) objects: human heads. From an ensemble of several hundred laser-scanned 3D heads, we use principal component analysis to derive a low-dimensional parameterization of head shape space. An algorithm for solving shape-from-shading using this representation is presented. It works well even on real images where it is able to recover the 3D surface for a given person, maintaining facial detail and identity, from a single 2D image of his face. This algorithm has applications in face recognition and animation.

Antigravity Slopes

2017 ◽  
Author(s):  
Kokichi Sugihara
Keyword(s):  
Human Brain ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Real Life ◽  
Two Dimensional ◽  
Single View ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
New Type ◽  
Law Of Gravity

A new type of illusion, called the antigravity slope illusion, is presented in this chapter. In this illusion a slope orientation is perceived opposite to the true orientation and hence a ball put on it appears to be rolling uphill, defying the law of gravity. This illusion is based on the ambiguity in the distance from a viewpoint to the surface of a three-dimensional solid represented in a single-view image. This illusion also arises in human real life, for example, when a car driver misunderstands the orientation of a road along which he or she is driving. Two assumptions are explored: (a) the human brain prefers to interpret vertical columns in a two-dimensional image as being vertical in three-dimensional space to being slanted and (b) the human brain prefers the most symmetric shape as the interpretation of a two-dimensional image.

Image Corrected Cephalometric Analysis (ICCA): Design and Evaluation

1993 ◽  
Vol 30 (6) ◽  
pp. 528-541 ◽  
Author(s):  
John L. Spolyar ◽  
William Vasileff ◽  
Robert B. Macintosh ◽  
Bodil Rune ◽  
John L. Spolyar
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Bilateral Symmetry ◽  
Bone Marker ◽  
Cephalometric Analysis ◽  
Two Dimensional ◽  
Midsagittal Plane ◽  
Two Dimensional Image ◽  
Marker Point ◽  
Serial Measurements

Image corrected cephalometric analysis (ICCA) Is a method for eliminating serial image parallax error. In a radiographic survey, image parallax is an inherent and random property of the two-dimensional Image of the subject. Radiographs of the same subject taken at different times will be different in image parallax. This difference, parallax error, is routinely displayed between serial radiographic studies. Parallax error discourages the use of conventional serial cephalometric surveys for tracking and studying changes in discrete craniofacial structures lying outside the midsagittal plane, unilaterally disposed, or changing without bilateral symmetry. Anatomic outlines or discrete points of such structures would routinely display measurement perturbations caused by image parallax differences between surveys. The ICCA method eliminates this problem. Therefore, accurate serial measurements of bone marker point displacements are made possible with two-dimensional reconstructions of points lying in three-dimensional space. The method of ICCA was tested for accuracy by using zero time serial cephalometric surveys of five subjects. Mean implant error of 0.12 mm (SD = 0.1) was found between predicted (ICCA) and actual measured Implant movement caused by the image parallax error. After applying this method, bone marker movements are unlikely to be caused by parallax error between conventional serial cephalometric studies. Furthermore, displacement growth can be related to the relocation of composite growth outlines and midline anatomic landmarks. One plagiocephaly case and one hemifacial microsomia case were used to demonstrate ICCA for growth and treatment effect documentation.

scholarly journals Spontaneous discrimination of possible and impossible objects by newly hatched chicks

2011 ◽  
Vol 7 (5) ◽  
pp. 654-657 ◽  
Author(s):  
Lucia Regolin ◽  
Rosa Rugani ◽  
Gionata Stancher ◽  
Giorgio Vallortigara
Keyword(s):  
Structural Information ◽  
Three Dimensional ◽  
Global Structure ◽  
Two Dimensional ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
Vertebrate Brain ◽  
Relative Contribution ◽  
Real Objects ◽  
Dimensional Object

Four-month-old infants can integrate local cues provided by two-dimensional pictures and interpret global inconsistencies in structural information to discriminate between possible and impossible objects. This leaves unanswered the issue of the relative contribution of maturation of biologically predisposed mechanisms and of experience with real objects, to the development of this capability. Here we show that, after exposure to objects in which junctions providing cues to global structure were occluded, day-old chicks selectively approach the two-dimensional image that depicted the possible rather than the impossible version of a three-dimensional object, after restoration of the junctions. Even more impressively, completely naive newly hatched chicks showed spontaneous preferences towards approaching two-dimensional depictions of structurally possible rather than impossible objects. These findings suggest that the vertebrate brain can be biologically predisposed towards approaching a two-dimensional image representing a view of a structurally possible three-dimensional object.

Reflection from Curved Mirrors in a Plane

2019 ◽  
Vol 7 (1) ◽  
pp. 46-54 ◽  
Author(s):  
Л. Жихарев ◽  
L. Zhikharev
Keyword(s):  
Dimensional Space ◽  
Spherical Surface ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Interesting Phenomenon ◽  
One Dimensional ◽  
Straight Line ◽  
The Family ◽  
Dimensional Object ◽  
Three Dimensional Space

Reflection from a certain mirror is one of the main types of transformations in geometry. On a plane a mirror represents a straight line. When reflecting, we obtain an object, each point of which is symmetric with respect to this straight line. In this paper have been considered examples of reflection from a circle – a general case of a straight line, if the latter is defined through a circle of infinite radius. While analyzing a simple reflection and generalization of this process to the cases of such curvature of the mirror, an interesting phenomenon was found – an increase in the reflection dimension by one, that is, under reflection of a one-dimensional object from the circle, a two-dimensional curve is obtained. Thus, under reflection of a point from the circle was obtained the family of Pascal's snails. The main cases, related to reflection from a circular mirror the simplest two-dimensional objects – a segment and a circle at their various arrangement, were also considered. In these examples, the reflections are two-dimensional objects – areas of bizarre shape, bounded by sections of curves – Pascal snails. The most interesting is the reflection of two-dimensional objects on a plane, because the reflection is too informative to fit in the appropriate space. To represent the models of obtained reflections, it was proposed to move into three-dimensional space, and also developed a general algorithm allowing obtain the object reflection from the curved mirror in the space of any dimension. Threedimensional models of the reflections obtained by this algorithm have been presented. This paper reveals the prospects for further research related to transition to three-dimensional space and reflection of objects from a spherical surface (possibility to obtain four-dimensional and five-dimensional reflections), as well as studies of reflections from geometric curves in the plane, and more complex surfaces in space.

scholarly journals Basic Stereology

2003 ◽  
Vol 11 (1) ◽  
pp. 12-17 ◽  
Author(s):  
John M. Basgen
Keyword(s):  
Mr Imaging ◽  
Internal Structure ◽  
Three Dimensional ◽  
Quantitative Information ◽  
Two Dimensional ◽  
Two Dimensional Image ◽  
Three Dimensional Objects ◽  
Different Types ◽  
Dimensional Object ◽  
Two Dimensional Images

Many us who use microscopes are interested in the internal structure or components of three-dimensional objects. Often we must section these objects to observe these internal components. For many years, microtomes have been used to make physical sections, but in recent years confocal microscopes, MR imaging, CT scanners, and even standard optical microscopes have been used to obtain “optical” sections. Two-dimensional images of these different types of sections can be used to extract three-dimensional quantitative information about the objects and their internal components, The sectioning process reduces the observed dimensions of the object and components. With apologies to Rene Magritte, the structure portrayed in Figure 1 is not a three-dimensional glomerulus but a two-dimensional profile of a glomerulus. In most cases, interest is on the structure of the three-dimensional object and not the structure in the two-dimensional image. Thus, care must be taken when obtaining and interpreting data from two-dimensional images.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

scholarly journals A Self-Established “Machining-Measurement-Evaluation” Integrated Platform for Taper Cutting Experiments and Applications

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 929
Author(s):  
Xudong Yang ◽  
Zexiao Li ◽  
Linlin Zhu ◽  
Yuchu Dong ◽  
Lei Liu ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Precision Machining ◽  
Two Dimensional ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
Integrated Platform ◽  
Hard And Brittle Materials ◽  
Ultra Precision ◽  
Cutting Experiments

Taper-cutting experiments are important means of exploring the nano-cutting mechanisms of hard and brittle materials. Under current cutting conditions, the brittle-ductile transition depth (BDTD) of a material can be obtained through a taper-cutting experiment. However, taper-cutting experiments mostly rely on ultra-precision machining tools, which have a low efficiency and high cost, and it is thus difficult to realize in situ measurements. For taper-cut surfaces, three-dimensional microscopy and two-dimensional image calculation methods are generally used to obtain the BDTDs of materials, which have a great degree of subjectivity, leading to low accuracy. In this paper, an integrated system-processing platform is designed and established in order to realize the processing, measurement, and evaluation of taper-cutting experiments on hard and brittle materials. A spectral confocal sensor is introduced to assist in the assembly and adjustment of the workpiece. This system can directly perform taper-cutting experiments rather than using ultra-precision machining tools, and a small white light interference sensor is integrated for in situ measurement of the three-dimensional topography of the cutting surface. A method for the calculation of BDTD is proposed in order to accurately obtain the BDTDs of materials based on three-dimensional data that are supplemented by two-dimensional images. The results show that the cutting effects of the integrated platform on taper cutting have a strong agreement with the effects of ultra-precision machining tools, thus proving the stability and reliability of the integrated platform. The two-dimensional image measurement results show that the proposed measurement method is accurate and feasible. Finally, microstructure arrays were fabricated on the integrated platform as a typical case of a high-precision application.

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