  Shape analysis and classification are popular methods for biologists,
biophysicists and mathematicians investigating relationships between object
function and form. Classic shape descriptors, such as sphericity, can be very
powerful; however, when evaluating complex shapes, these descriptors can be
insufficient for rigorous assessment. Here, we present "ToSkA: Topological
Skeleton Analysis" a method to analyse complex objects by representing their
shape asymmetries as networks. Using global neighbourhood principles, classic
network science metrics and spatial feature embedding we are able to create
unique object profiles for classification. It is also possible to track objects
over time and extract significantly different shape features between
experiments. Importantly, we have incorporated the capacity to measure absolute
spatial features of objects (e.g., branch lengths). This adds additional layers
of sensitivity to object classification. Furthermore, because topology is an
inherent property of system identity, ToSkA is able to identify segmentation
errors that alter object topology by observing the emergence or loss of cycles
in network representations. Combined, the analytics of ToSkA presented here
allow for the flexibility and in-depth shape profiling necessary for complex
objects often observed in biological and physical settings where robust, yet
precise, system configuration is essential to downstream processes.
