Perception of solid shape from shading

Observers judged the slants and tilts of numerous regions within shaded images of ellipsoid surfaces that varied in shape, orientation, surface reflectance, and direction of illumination. The perceived three-dimensional structure of each surface was calculated from these judgments. Much of the error in observers' responses resulted from a tendency to perceive surfaces whose axes were aligned with the display screen. The presence of specular highlights or cast shadows, in contrast, had no effect on performance. The results of the experiment indicate that several assumption of certain formal models for perception of shape from shading are not psychologically valid. The most notable of these assumptions are that the visual system initially assumes that all surfaces have Lambertian reflectance and that illuminant direction must be known before shape detection can proceed. These assumptions are often accompanied by a third assumption that surface orientation is detected locally, and global shape determined by smoothing over local surface orientation estimates. The present experiment indicates that an alternative approach offered by Koenderink and van Doorn may be more psychologically accurate, as it avoids all three assumptions.Supported in part by the Air Force Office of Scientific Research (AFOSR 82-0148). The research reported in this paper was performed while the first author was a graduate student at the University of Connecticut at Storrs     

A Model of Cell Cleavage

A model is presented which describes, at least to a first approximation, the oserved changes in cell shape and the movement of surface markers associated with cleavage in some types of cells. The model postulates that the constraints governing cell cleavage are minimum surface area and constancy of cell volume. Equations are derived both for the case of symmetric as well as the case of asymmetric cleavage. It is pointed out that the generally symmetric character of cell cleavage is explicable if there is a positive correlation between internal cell pressure and the radii of curvature.     

Shape information from shading: a theory about human perception

I present evidence that people assume a simple, linear reflectance function when interpreting shading information. Using this reflectance function I derive a closed-form solution to the problem of extracting shape information from image shading. The solution does not employ an assumption about surface smoothness and so is directly applicable to complex natural surfaces such as hair or cloth. A simple biological mechanism is proposed to implement this recovery of shape. It is shown that this simple mechanism can also extract significant shape information from line drawings.     

Shape from texture

A central goal for visual perception is the recovery of the three-dimensional structure of the surfaces depicted in an image. Crucial information about three-dimensional structure is provided by the spatial distribution of surface markings, particularly for static monocular views: projection distorts texture geometry in a manner tha depends systematically on surface shape and orientation. To isolate and measure this projective distortion in an image is to recover the three dimensional structure of the textured surface. For natural textures, we show that the uniform density assumption (texels are uniformly distributed) is enough to recover the orientation of a single textured plane in view, under perspective projection. Furthermore, when the texels cannot be found, the edges of the image are enough to determine shape, under a more general assumption, that the sum of the lengths of the contours on the world plane is about the same everywhere. Finally, several experimental results for synthetic and natural images are presented.     

Effects of substratum morphology on cell physiology

Among the host of substratum properties that affect animal cell behavior, surface morphology has received relatively little attention. The earliest effect of surface morphology on animal cells was discovered almost a century ago when it was found that cells became oriented in response to the underlying topography. This phenomenon is now commonly known as contact guidance. From then until very recentrly, little progress has been made in understanding the role of surface morphology on cell behavior, primarily due to a lack of defined surfaces with uniform morphologies. This problem has been solved recently with the development of photolithographic techniques to prepare substrata with well defined and uniform surface morphologies. Availability of such surfaces has facilitated systematic in vitro experiments to study influence of surface morphology on diverse cell physiological aspects such as adhesion, growth, and function. For example, these studies have shown that surfaces with uniform multipls parallel grooves can enhance cell adhesion by confining cells in grooves and by mechanically interlocking them. Several independent studies have demosterated that cell shape is a major determinant of cell growth and function. Because surface morphology has been shown to modulate the extent of cell spreading and cell shape, its effects on cell growth and function appear to be mediated via this biological coupling between cell shape and function. New evidence in the cell biology literature is emerging to suggest that surface morphology could affect other cell behavioral properties such as post-translational modifications. Further elucidation of such effects will enable better designs for implant and cell culture substrata.     

A two-dimension otolith growth inverse model

An inverse growth model was developed to describe fish otolith ontogenetic growth to find the most parsimonious growth field that drives the actual shape of an internal incremental structure to the actual external shape of the otolith. This approach is based in a pure physic model, and the single implicit assumption was that the otolith accretion occurred perpendicular to its external surface. The model could be used to define a general hypothesis situation, in the sense that it predicts the most plausible shape of the otolith at any time, assuming that no additional external forces have acted. Therefore, severe departures between the observed growth structure and the closest prediction to it could be used to identify anatomical constraints and physiological factors that modulate the pure physical expectations.     

Mathematical description of the stimuli to the lateral line system of fish derived from a three-dimensional flow field analysis

The three-dimensional potential flow field around a moving fish with an axially symmetric body is investigated mathematically. The case of a moving fish in open water and that of one approaching a plane surface in front of it are considered. For these cases the spatial and temporal distributions of the stimuli to the lateral line system are derived from the flow field analysis. This is done in dependence on the shape and the size of the fish.     

Superquadric modeling of cranial and cerebral shape and asymmetry

A new method for quantifying cranial and cerebral shape and asymmetry fits symmetric superquadric geometric models to three-dimensional coordinate measurements. Asymmetry is quantified as radial residuals of the surface data points from their best-fit superquadric models. Twenty human crania, 10 magnetic resonance imaging (MRI) exocranial surfaces, and 10 corresponding MRI cerebral surfaces as well as two infant head casts were digitized and modeled using superquadrics. Superquadric parameters have simple geometric interpretation, are very reproducible, and demonstrated statistically significant differences between crania of Amerindian ancestry and MRI exocranial surfaces of European ancestry used in this study. Superquadric models demonstrated strong congruence between MRI exocranial and cerebral surfaces. Typical asymmetry was 1-5 mm. Lastly, polar contour plots of radial residuals for head casts before and after orthotic cranioplasty demonstrated the efficacy of using superquadrics to quantify positional plagiocephaly and synostosis of infant crania.     

Patient-specific acetabular shape modelling: comparison among sphere,ellipsoid and conchoid parameterisations

The shape of the human acetabular cup was commonly represented as a hemisphere, but different geometries and patient-specific shapes have been recently proposed in the literature. Our aim was to test the limits of the sphericity assumption by comparing three different parameterisations, namely the sphere, the ellipsoid and the rotational conchoid. Models of hip surfaces, reconstructed from CT scans taken from Caucasian race cadavers and patients, were automatically processed to extract the acetabular surface. Two separate analyses were carried out on the overall acetabular shape, including both the acetabular fossa and the lunate surface (case A) and acetabular cup represented by the lunate surface only (case B). Nonlinear gradient-based and evolutionary computation approaches were implemented for the fitting process. Minor differences from the three idealised geometries were detected (median values of the fitting errors < 1 mm). Nonetheless, the sphere fitting was found to be statistically different from both the ellipsoid (p < 2.50e ? 10) and the conchoid (p < 1.07e ? 09), whereas no statistical difference was detected between the ellipsoid and the conchoid for case A. Significance of the difference between ellipsoid and sphere (p < 4.55e ? 12) and between conchoid and sphere (p < 1.93e ? 11) was found for case B as well. Interestingly, for case B statistical difference was detected between the ellipsoid and the conchoid. In conclusion, we synthesise that the morphology of the overall acetabular cup can be parameterised both with an ellipsoid shape and with a conchoid shape as well with superior quality than the simple sphere. Differently, if one considers just the lunate surface, better fitting results are expected when using the ellipsoid.     

Listeria monocytogenes LO28: surface physicochemical properties and ability to form biofilms at different temperatures and growth phases

The surface physicochemical properties of Listeria monocytogenes LO28 under different conditions (temperature and growth phase) were determined by use of microelectrophoresis and microbial adhesion to solvents. The effect of these parameters on adhesion and biofilm formation by L. monocytogenes LO28 on hydrophilic (stainless steel) and hydrophobic (polytetrafluoroethylene [PTFE]) surfaces was assessed. The bacterial cells were always negatively charged and possessed hydrophilic surface properties, which were negatively correlated with growth temperature. The colonization of the two surfaces, monitored by scanning electron microscopy, epifluorescence microscopy, and cell enumeration, showed that the strain had a great capacity to colonize both surfaces whatever the incubation temperature. However, biofilm formation was faster on the hydrophilic substratum. After 5 days at 37 or 20 degrees C, the biofilm structure was composed of aggregates with a three-dimensional shape, but significant detachment took place on PTFE at 37 degrees C. At 8 degrees C, only a bacterial monolayer was visible on stainless steel, while no growth was observed on PTFE. The growth phase of bacteria used to inoculate surfaces had a significant effect only in some cases during the first steps of biofilm formation. The surface physicochemical properties of the strain are correlated with adhesion and surface colonization.     

Hydrocarbon fermentations using Candida lipolytica. II. A model for cell growth kinetics

A mechanistic model is presented for the growth kinetics of a yeast grown by submerged aerobic fermentation using a liquid hydrocarbon as sole carbon source. The model is based on the assumption that cell growth is governed by the extent of probable cell attachment at the hydrocarbon oil-droplet surfaces in a four-phase dispersion. An analytical expression has been developed for the model. It is shown that for the case of relatively small oil droplets, the model predicts the present and previous experimental data for growth of yeasts (Candida species) in n-alkane systems. The model is further examined for maximal growth in terms of substrate dilution rate and agitation power consumption for a continuous fermentation process.     

A spatial mechanism with higher pairs for modelling the human knee joint

By generalizing a previous model proposed in the literature, a new spatial kinematic model of the knee joint passive motion is presented. The model is based on an equivalent spatial parallel mechanism which relies upon the assumption that fibers within the anterior cruciate ligament (ACL), the medial collateral ligament (MCL) and the posterior cruciate ligament (PCL) can be considered as isometric during the knee flexion in passive motion (virtually unloaded motion). The articular surfaces of femoral and tibial condyles are modelled as 3-D surfaces of general shapes. In particular, the paper presents the closure equations of the new mechanism both for surfaces represented by means of scalar equations that have the Cartesian coordinates of the points of the surface as variables and for surfaces represented in parametric form. An example of simulation is presented in the case both femoral condyles are modelled as ellipsoidal surfaces and tibial condyles as spherical surfaces. The results of the simulation are compared to those of the previous models and to measurements. The comparison confirms the expectation that a better approximation of the tibiofemoral condyle surfaces leads to a more accurate model of the knee passive motion.     

Theory of equilibrium binding of symmetric bivalent haptens to cell surface antibody: application to histamine release from basophils.

We present a theory of equilibrium binding of symmetric bivalent haptens to cell surface antibody in the presence or absence of monovalent hapten. Bivalent haptens can link together antibodies to form linear chains or rings on cell surfaces. We show how to calculate the amount of any complex of bound bivalent hapten, monovalene fraction of antibody involved in complexes made up of two or more antibodies, i.e., the fraction of antibody that is cross-linked (Xpoly). We treat the case when the antibody on the cell surface, which is specific for the hapten, is homogeneous. For this case we prove a number of general properties about Xpoly: 1) Xpoly approaches zero at both high and low bivalent hapten concentration. 2) Xpoly becomes a maximum when the bivalent hapten concentration equals Amax, where Amax = 1/H + B/2. H is twice the equilibrium constant for the binding of a single hapten site to a single antibody site and B is the monovalent hapten concentration. 3) a plot of Xpoly vs the log of the bivalent hapten concentration is symmetric about the maximum value of Xpoly. We use these and other properties of Xpoly in this paper to clarify the relationship between cross-link formation and histamine release.     

An elastic model of the large-scale structure of duplex DNA.

A general model for the large-scale, time-independent structure of duplex DNA is developed based on elastic considerations. The general conditions of elastic equilibrium are given. These equations are solved for the equilibrium shape of stressed duplex DNA, based on the assumption that the double helix behaves mechanically as a symmetric, linearly elastic rod. It is shown that, in general, two orders of superhelicity will arise at equilibrium. Several possible applications of this approach to the supercoiling of closed circular DNA are described.     

Equilibrium surface charge distribution in phospholipid vesicles. I. Method of calculation

This paper presents a method of calculation of the surface charge equilibrium distribution between the two surfaces of a spherically closed phospholipid bilayer suspended in aqueous electrolyte solution. The net surface charge is supposed to be provided by the ionized polar groups of the phospholipid molecules. Its equilibrium distribution is found by minimization of the free electrostatic energy. The procedure of minimization utilizes the solution of the Poisson-Boltzmann equation which describes the double electric layers of the membrane and an expression for the membrane potential derived under the assumption of absence of charges in the membrane phase. An analytical solution of the problem in the range of validity of the linearized Poisson-Boltzman equation is obtained. It is shown that in this case an equilibrium transmembrane potential exists, and the surface charge density is greater at the outer surface of the vesicle.     

Listeria monocytogenes LO28: Surface Physicochemical Properties and Ability To Form Biofilms at Different Temperatures and Growth Phases

The surface physicochemical properties of Listeria monocytogenes LO28 under different conditions (temperature and growth phase) were determined by use of microelectrophoresis and microbial adhesion to solvents. The effect of these parameters on adhesion and biofilm formation by L. monocytogenes LO28 on hydrophilic (stainless steel) and hydrophobic (polytetrafluoroethylene [PTFE]) surfaces was assessed. The bacterial cells were always negatively charged and possessed hydrophilic surface properties, which were negatively correlated with growth temperature. The colonization of the two surfaces, monitored by scanning electron microscopy, epifluorescence microscopy, and cell enumeration, showed that the strain had a great capacity to colonize both surfaces whatever the incubation temperature. However, biofilm formation was faster on the hydrophilic substratum. After 5 days at 37 or 20°C, the biofilm structure was composed of aggregates with a three-dimensional shape, but significant detachment took place on PTFE at 37°C. At 8°C, only a bacterial monolayer was visible on stainless steel, while no growth was observed on PTFE. The growth phase of bacteria used to inoculate surfaces had a significant effect only in some cases during the first steps of biofilm formation. The surface physicochemical properties of the strain are correlated with adhesion and surface colonization.     

Extent of structural asymmetry in homodimeric proteins: prevalence and relevance

Most homodimeric proteins have symmetric structure. Although symmetry is known to confer structural and functional advantage, asymmetric organization is also observed. Using a non-redundant dataset of 223 high-resolution crystal structures of biologically relevant homodimers, we address questions on the prevalence and significance of asymmetry. We used two measures to quantify global and interface asymmetry, and assess the correlation of several molecular and structural parameters with asymmetry. We have identified rare cases (11/223) of biologically relevant homodimers with pronounced global asymmetry. Asymmetry serves as a means to bring about 2:1 binding between the homodimer and another molecule; it also enables cellular signalling arising from asymmetric macromolecular ligands such as DNA. Analysis of these cases reveals two possible mechanisms by which possible infinite array formation is prevented. In case of homodimers associating via non-topologically equivalent surfaces in their tertiary structures, ligand-dependent mechanisms are used. For stable dimers binding via large surfaces, ligand-dependent structural change regulates polymerisation/depolymerisation; for unstable dimers binding via smaller surfaces that are not evolutionarily well conserved, dimerisation occurs only in the presence of the ligand. In case of homodimers associating via interaction surfaces with parts of the surfaces topologically equivalent in the tertiary structures, steric hindrance serves as the preventive mechanism of infinite array. We also find that homodimers exhibiting grossly symmetric organization rarely exhibit either perfect local symmetry or high local asymmetry. Binding of small ligands at the interface does not cause any significant variation in interface asymmetry. However, identification of biologically relevant interface asymmetry in grossly symmetric homodimers is confounded by the presence of similar small magnitude changes caused due to artefacts of crystallisation. Our study provides new insights regarding accommodation of asymmetry in homodimers.     

A computer simulation of surface microcolony formation during microbial colonization

Several models of microbial surface colonization have been devised to quantitate growth and attachment rates on surfaces. One of these, the surface growth rate equation, is based on the assumption that the number of microcolonies of a given size (C_i) reaches a constant value (C_max) that is equal to the attachment rate (A) divided by the specific growth rate (Μ). In this study, a computer simulation was used to determine the time required to reach C_max. It was shown that C_i approaches C_max asymptotically. The time required is dependent solely upon the growth rate and size of microcolonies. The number of one-celled microcolonies reaches 95% of C_max after 4.3 generations. At low growth rates, a relatively long incubation period is required. Alternate methods that shorten the incubation time are considered.     

Cell-Shape Regulation of Smooth Muscle Cell Proliferation

Vascular smooth muscle cells (SMCs) play an important role in vascular remodeling. Heterogeneity and phenotypic changes in SMCs are usually accompanied by a morphological difference, i.e., elongated/spindle-like versus spread-out or epithelioid/rhomboid cell shapes. However, it is not known whether the cell shape directly regulates SMC proliferation, and what the underlying mechanisms are. In this study, microgrooves and micropatterned matrix islands were used to engineer the cell shape and investigate the associated biophysical and biological mechanisms. Compared to spread-out SMCs on nonpatterned surfaces, SMCs on micropatterned surfaces demonstrated elongated morphology, significantly lower cell and nucleus shape indexes, less spreading, a lower proliferation rate, and a similar response (but to a lesser extent) to platelet-derived growth factor, transforming growth factor-β, and mechanical stretching. DNA microarray profiling revealed a lower expression of neuron-derived orphan receptor-1 (NOR-1) in elongated SMCs. Knocking down NOR-1 suppressed DNA synthesis in SMCs, suggesting that NOR-1 is a mediator of cell elongation effects. Regulation of DNA synthesis in SMCs by the cell shape alone and a decrease in DNA synthesis in the case of small cell spreading area were achieved by micropatterning SMCs on matrix islands of different shapes and spreading areas. Changes in the cell shape also affected the nucleus shape, whereas variations in the cell spreading area modulated the nucleus volume, indicating a possible link between nucleus morphology (both shape and volume) and DNA synthesis. The findings of this investigation provide insight into cell shape effects on cell structure and proliferation, and have direct implications for vascular pathophysiology.