This study considers the problem of describing and predicting cleft formation during the early stages of branching morphogenesis in mouse submandibular salivary glands (SMG) under the influence of varied concentrations of epidermal growth factors (EGF). Given a time-lapse video of a growing SMG, first we build a descriptive model that captures the underlying biological process and quantifies the ground truth. Tissue-scale (global) and morphological features related to regions of interest (local features) are used to characterize the biological ground truth. Second, we devise a predictive growth model that simulates EGF-modulated branching morphogenesis using a dynamic graph algorithm, which is driven by biological parameters such as EGF concentration, mitosis rate, and cleft progression rate. Given the initial configuration of the SMG, the evolution of the dynamic graph predicts the cleft formation, while maintaining the local structural characteristics of the SMG. We determined that higher EGF concentrations cause the formation of higher number of buds and comparatively shallow cleft depths. Third, we compared the prediction accuracy of our model to the Glazier-Graner-Hogeweg (GGH) model, an on-lattice Monte-Carlo simulation model, under a specific energy function parameter set that allows new rounds of de novo cleft formation. The results demonstrate that the dynamic graph model yields comparable simulations of gland growth to that of the GGH model with a significantly lower computational complexity. Fourth, we enhanced this model to predict the SMG morphology for an EGF concentration without the assistance of a ground truth time-lapse biological video data; this is a substantial benefit of our model over other similar models that are guided and terminated by information regarding the final SMG morphology. Hence, our model is suitable for testing the impact of different biological parameters involved with the process of branching morphogenesis in silico, while reducing the requirement of in vivo experiments.

Cleft formation during submandibular salivary gland branching morphogenesis is the critical step initiating the growth and development of the complex adult organ. Previous experimental studies indicated requirements for several epithelial cellular processes, such as proliferation, migration, cell-cell adhesion, cell-extracellular matrix (matrix) adhesion, and cellular contraction in cleft formation; however, the relative contribution of each of these processes is not fully understood since it is not possible to experimentally manipulate each factor independently. We present here a comprehensive analysis of several cellular parameters regulating cleft progression during branching morphogenesis in the epithelial tissue of an early embryonic salivary gland at a local scale using an on lattice Monte-Carlo simulation model, the Glazier-Graner-Hogeweg model. We utilized measurements from time-lapse images of mouse submandibular gland organ explants to construct a temporally and spatially relevant cell-based 2D model. Our model simulates the effect of cellular proliferation, actomyosin contractility, cell-cell and cell-matrix adhesions on cleft progression, and it was used to test specific hypotheses regarding the function of these parameters in branching morphogenesis. We use innovative features capturing several aspects of cleft morphology and quantitatively analyze clefts formed during functional modification of the cellular parameters. Our simulations predict that a low epithelial mitosis rate and moderate level of actomyosin contractility in the cleft cells promote cleft progression. Raising or lowering levels of contractility and mitosis rate resulted in non-progressive clefts. We also show that lowered cell-cell adhesion in the cleft region and increased cleft cell-matrix adhesions are required for cleft progression. Using a classifier-based analysis, the relative importance of these four contributing cellular factors for effective cleft progression was determined as follows: cleft cell contractility, cleft region cell-cell adhesion strength, epithelial cell mitosis rate, and cell-matrix adhesion strength.

In this paper, we introduce a biologically motivated dynamic graph-based growth model to describe and predict the stages of cleft formation during the process of branching morphogenesis in the submandibular mouse gland (SMG) from 3 hrs after embryonic day E12 to 8 hrs after embryonic day E12, which can be considered as E12.5. Branching morphogenesis is the process by which many mammalian exocrine and endocrine glands undergo significant morphological transformations, from a primary bud to an adult organ. Although many studies have investigated the cellular and molecular mechanisms driving branching morphogenesis, it is not clear how the shape changes that are inherent to establishing organ structure are produced. Using morphological features extracted from sequential images of SMG organ cultures we were able to develop a dynamic graph-based predictive model that is able to mimic the process of cleft formation and predict the final state. In addition, we compare our model to a state-of-the-art Glazier-Graner-Hogeweg (GGH) simulative tool, and demonstrate that the dynamic graph-based predictive model has comparable accuracy in modeling growth of clefts across SMG developmental stages, as well as faster convergence to the target SMG morphology.

We present a method for embedding and detection of visual watermark patterns in printed images that use clustered-dot halftones in the printing process. The method allows two independent watermark patterns to be multiplexed, i.e. embedded in the same region of the printed image, thereby offering an improvement over prior techniques. The watermark patterns are embedded via phase modulation along the two periodicity directions of the halftone. Each embedded pattern can be visually detected, without interference from the other watermark, when the printed image, or a scan thereof, is overlaid with a decoder mask consisting of periodic lines oriented along the corresponding halftone periodicity direction. We experimentally demonstrate that our proposed multiplexing technique is effective. We also present analysis that demonstrates that the embedding has minimal visual impact and explains the pattern observed in the watermark detection process.

A generalization of periodic clustered-dot halftones is proposed, wherein the phase of the halftone spots is modulated using a secondary signal. The process is accomplished by using an analytic halftone threshold function that allows halftones to be generated with controlled phase variation in different regions of the printed page. The method can also be used to modulate the screen frequency, albeit with additional constraints. Visible artifacts are minimized/eliminated by ensuring the continuity of the modulation in phase. Limitations and capabilities of the method are analyzed through a quantitative model. The technique can be exploited for two applications that are presented in this paper: a) embedding watermarks in the halftone image by encoding information in phase or in frequency and b) modulating the screen frequency according to the frequency content of the continuous tone image in order to improve spatial and tonal rendering. Experimental performance is demonstrated for both applications.

Misregistration between the color separations of a printed image, which is often inevitable, can cause objectionable color shifts in average color. We analyze the impact of inter-separation misregistration on clustered-dot halftones using Fourier analysis in a lattice framework. Our analysis provides a complete characterization of the conditions under which the average color is invariant to displacement misregistration. In addition to known conditions on colorant spectra and periodicity of the halftones, the work reveals that invariance can also be obtained when these conditions are violated for suitable dot shapes and displacements. Examples for these conditions are included, as is the consideration of traditional halftone configurations.

We propose a generalization of periodic clustered-dot halftones, wherein the phase of the halftones is modulated using a secondary signal. The process is accomplished using an analytic halftone threshold function and allows halftones to be generated with different phase variation in different regions of the printed page. We demonstrate that ensuring continuity of the phase assures that the resulting halftone images are free from visible artifacts despite the modulation in phase. We present, applications of the proposed method to halftone data embedding, wherein the changes in phase or in frequency encode the embedded information. For the frequency embedding, using continuous phase modulation, we also consider the limitations on signals that are embedded within our framework. For both applications, we demonstrate how the embedded signals may be recovered from the printed halftones either using the image as a self-reference which reveals the watermark when it is shifted and overlaid with itself or by employing a separate transparency mask

We propose an analytic method to overcome the trade-off between the spatial and tonal resolution of traditional clustered dot halftones. Continuous phase modulated halftones that allow variations in screen frequency in different regions of the printed image are employed and halftone screen frequency is varied according to the frequency content of the image to be halftoned. The method, which we term self-modulated halftoning, has a computational complexity similar to screening and is significantly lower than that of other adaptive methods that have previously been used to address the same problem. We demonstrate the experimental performance of self-modulated halftones and discuss its capabilities and limitations.