Chapter 8 – Theoretical Biophysics  369

Light microscopy bright-​field images of cells and tissues, even using enhancement

methods such as phase contrast or DIC (see Chapter 3), result in diffraction-​limited blurring

of the cellular boundary and of higher length scale tissue structures. Several image segmen­

tation techniques are available that can determine the precise boundaries of cells and tissue

structures. These enable cell bodies and structures to be separately masked out and subjected

to further image analysis, in addition to generating vital statistics of cell and tissue structure

dimensions. Vital statistics are valuable for single-​cell imaging in model bacteria in being used

to perform coordinate transformations between the Cartesian plane of the camera detector

and the curved surface of a cell, for example, if tracking the diffusion of a membrane protein

on the cell’s surface. The simplest and most computationally efficient method involves pixel

intensity thresholding that in essence draws a contour line around a cell image corresponding

to a preset pixel intensity value, usually interpolated from the raw pixel data. Such methods

are fast and reliable if the cell body pixel intensity distribution is homogeneous.

Often cell images are very close to each other to the extent that they are essentially

touching, for example, cell-​to-​cell adhesions in a complex multicellular tissue or recent

cell division events in the case of observation on isolated cells. In these instances simple

pixel thresholding tools will often fail to segment these proximal cells. Watershed methods

can overcome this problem by utilizing “flooding” strategies. Flooding seed points are first

determined corresponding roughly to the center of putative cell objects, and the image is

flooded with additional intensity added to pixel values radially from these seeds until two

juxtaposed flooding wave fronts collide. This collision interface then defines the segmenta­

tion boundary between two proximal cells.

The most robust but computationally expensive cell image segmentation methods utilize

prior knowledge of what the sizes and shapes of the specific cells under investigation are

likely to be. These can involve Bayesian inference tools utilizing prior knowledge from pre­

vious imaging studies, and many of these approaches use maximum entropy approaches to

generate optimized values for segmentation boundaries. Similarly, maximum a posteriori

methods using Bayesian statistics operate by minimizing an objective energy function

obtained from the raw image data to determine the most likely position of cell boundaries.

KEY POINT 8.9

Information entropy is a numerical measure that describes how uninformative a par­

ticular probability distribution is, ranging from a minimum of zero that is completely

informative up to log(m), which is completely uninformative, where m is the number

of mutually exclusive propositions to choose from. The principle of maximum entropy

optimizes parameters in any given model on the basis that the information entropy is

maximized and thus results in the most uninformative probability distribution possible

since choosing a distribution that has lower entropy would assume information that is

not possessed.

Many molecular structures visualized in biological specimens using high-​spatial-​resolution

imaging techniques such as EM, AFM, and super-​resolution light microscopy may exhibit a

distribution on their orientation in their image data, for example, due to random orientation

of the structure in the specimen itself and/​or to random orientation of cells/​tissues in the

sample with respect to the imaging plane. To facilitate identification of such structures, there

are algorithms that can rotate images and compare them with reference sources to compare

in computationally efficient ways. This usually involves maximum likelihood methods that

generate a pixel-​by-​pixel cross-​correlation function between the candidate-​rotated image

and the reference source and find solutions that optimize the maximum cross-​correlation,

equivalent to template matching.

However, the most widely used method to recognize specific shapes and other topological

and intensity features of images is principal component analysis (PCA). The general method