J. Andrew Bangham

Growth dynamics underlying petal shape and asymmetry.

Development commonly involves the generation of complex shapes from simpler ones. One way of following this process is to use landmarks to track the fate of particular points in a developing organ, but this is limited by the time over which it can be monitored. Here we use an alternative method, clonal analysis, whereby dividing cells are genetically marked and their descendants identified visually, to observe the development of Antirrhinum (snapdragon) petals. Clonal analysis has previously been used to estimate growth parameters of leaves and Drosophila wings but these results were not integrated within a dynamic growth model. Here we develop such a model and use it to show that a key aspect of shape—petal asymmetry—in the petal lobe of Antirrhinum depends on the direction of growth rather than regional differences in growth rate. The direction of growth is maintained parallel to the proximodistal axis of the flower, irrespective of changes in shape, implying that long-range signals orient growth along the petal as a whole. Such signals may provide a general mechanism for orienting growth in other growing structures.

Genetic Control of Organ Shape and Tissue Polarity

A combination of experimental analysis and mathematical modelling shows how the genetic control of tissue polarity plays a fundamental role in the development and evolution of form.

Morphological scale-space preserving transforms in many dimensions

The theory of an image decomposition that we refer to as a sieve is developed for images defined in any finite number of dimensions. The decomposition has many desirable properties in- cluding the preservation of scale-space causality and the localiza- tion of sharp-edged objects in the transformation domain. The de- composition has the additional properties of manipulability, which means that it is easy to construct pattern recognition systems, and scale-calibration, which means that it may be used for accurate measurement.

Quantitative Control of Organ Shape by Combinatorial Gene Activity

A novel combination of molecular genetics, shape analysis, and computational modelling shows how the complex three-dimensional shape of the Snapdragon flower can arise through local gene activity.

Data-sieving hydrophobicity plots

Hydrophobicity plots provide clues to the tertiary structure of proteins (J. Kyte and R. F. Doolittle, 1982, J. Mol. Biol. 157, 105; C. Chothia, 1984, Annu. Rev. Biochem. 53, 537; T. P. Hopp and K. R. Woods, 1982, Proc. Natl. Acad. Sci. USA 78, 3824). To render domains more visible, the raw data are usually smoothed using a running mean of between 5 and 19 amino acids. This type of smoothing still incorporates two disadvantages. First, peculiar residues that do not share the properties of most of the amino acids in the domain may prevent its identification. Second, as a low-pass frequency filter the running mean smoothes sudden transitions from one domain, or phase, to another. Data-sieving is described here as an alternative method for identifying domains within amino acid sequences. The data-sieve is based on a running median and is characterized by a single parameter, the mesh size, which controls its resolution. It is a technique that could be applied to other series data and, in multidimensions, to images in the same way as a median filter.

Multiscale median and morphological filters for 2D pattern recognition

Abstract Experiments demonstrate a multiscale decomposition that complements those using standard linear functions. It binds edges rather than waves to features of different scales. The configuration of non-linear median or alternating sequential filters, ‘morphological filters’, used for the decomposition is referred to as a ‘sieve’. Results suggest that whilst some sieves produce an invertible transform, others have better statistical behaviour. Sieves are appropriate for isolating and locating the position of objects with sharp edges arising from nonlinear events such as occlusion. They represent shape information in a way that is independent of spatial frequency, that has different uncertainty trade-offs, and can be used for signal analysis and pattern recognition. For example, by matching the granularity of an image with the granularity of a target pattern, a simple pattern selective system (matched sieve) can be implemented that outperforms its linear analogue, a matcher filter. A sieve is a good multiscale smoother that improves upon single step standard median and morphological filters and is particularly appropriate for discontinuous signals, such as images where edges must be preserved.

The Segmentation of Images via Scale-Space Trees

A useful representation of an image would be an object tree in which nodes represent objects, or parts of objects, and which includes at least one node that, together with its children, represents each object: a grandmothernode. It is shown that scale-trees, obtained from greyscale images, approximate such a tree. It is then shown how they may be modified using other attributes to more closely become object trees. The result is a data structure that provides “handles” for every element of the image that can be used for manipulating the image. This segmentation has potential for object recognition.

A Comparison of Active Shape Model and Scale Decomposition Based Features for Visual Speech Recognition

Two quite different strategies for characterising mouth shapes for visual speech recognition (lipreading) are compared. The first strategy extracts the parameters required to fit an active shape model (ASM) to the outline of the lips. The second uses a feature derived from a one-dimensional multiscale spatial analysis (MSA) of the mouth region using a new processor derived from mathematical morphology and median filtering. With multispeaker trials, using image data only, the accuracy is 45% using MSA and 19% using ASM on a letters database. A digits database is simpler with accuracies of 77% and 77% respectively. These scores are significant since separate work has demonstrated that even quite low recognition accuracies in the vision channel can be combined with the audio system to give improved composite performance [16].

Generation of shape complexity through tissue conflict resolution

Out-of-plane tissue deformations are key morphogenetic events during plant and animal development that generate 3D shapes, such as flowers or limbs. However, the mechanisms by which spatiotemporal patterns of gene expression modify cellular behaviours to generate such deformations remain to be established. We use the Snapdragon flower as a model system to address this problem. Combining cellular analysis with tissue-level modelling, we show that an orthogonal pattern of growth orientations plays a key role in generating out-of-plane deformations. This growth pattern is most likely oriented by a polarity field, highlighted by PIN1 protein localisation, and is modulated by dorsoventral gene activity. The orthogonal growth pattern interacts with other patterns of differential growth to create tissue conflicts that shape the flower. Similar shape changes can be generated by contraction as well as growth, suggesting tissue conflict resolution provides a flexible morphogenetic mechanism for generating shape diversity in plants and animals. DOI: http://dx.doi.org/10.7554/eLife.20156.001

Scale-Space Filters and Their Robustness

We discuss some properties of a class of scale-space processors called sieves which are useful because, like a diffusion processor, they have an increasing support region, but, unlike a diffusion processor, the region follows extremal regions in the image. We test their robustness to noise and occlusion.