Julio Rubio

Jónathan Heras, Gadea Mata, Germán Cuesto et al.

Automation and reliability are the two main requirements when computers are applied in Life Sciences. In this paper we report on an application to neuron recognition, an important step in our long-term project of providing software systems to the study of neural morphology and functionality from biomedical images. Our algorithms have been implemented in an ImageJ plugin called NeuronPersistentJ, which has been validated experimentally. The soundness and reliability of our approach are based on the interpretation of our processing methods with respect to persistent homology, a well-known tool in computational mathematics.

Gadea Mata, Jónathan Heras, Miguel Morales et al.

The quantification of synapses is instrumental to measure the evolution of synaptic densities of neurons under the effect of some physiological conditions, neuronal diseases or even drug treatments. However, the manual quantification of synapses is a tedious, error-prone, time-consuming and subjective task; therefore, tools that might automate this process are desirable. In this paper, we present SynapCountJ, an ImageJ plugin, that can measure synaptic density of individual neurons obtained by immunofluorescence techniques, and also can be applied for batch processing of neurons that have been obtained in the same experiment or using the same setting. The procedure to quantify synapses implemented in SynapCountJ is based on the colocalization of three images of the same neuron (the neuron marked with two antibody markers and the structure of the neuron) and is inspired by methods coming from Computational Algebraic Topology. SynapCountJ provides a procedure to semi-automatically quantify the number of synapses of neuron cultures; as a result, the time required for such an analysis is greatly reduced.

Ana Romero, Julio Rubio, Francis Sergeraert

In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been implemented as extensions of the Kenzo system and have shown a good performance when applied on some actual images extracted from a public dataset.

Jónathan Heras, Gadea Mata, Ana Romero et al.

Fiji is a Java platform widely used by biologists and other experimental scientists to process digital images. In particular, in our research - made together with a biologists team; we use Fiji in some pre-processing steps before undertaking a homological digital processing of images. In a previous work, we have formalised the correctness of the programs which use homological techniques to analyse digital images. However, the verification of Fiji's pre-processing step was missed. In this paper, we present a multi-tool approach filling this gap, based on the combination of Why/Krakatoa, Coq and ACL2.

Jónathan Heras, María Poza, Julio Rubio

In this paper, we present a formalization of an algorithm to construct admissible discrete vector fields in the Coq theorem prover taking advantage of the SSReflect library. Discrete vector fields are a tool which has been welcomed in the homological analysis of digital images since it provides a procedure to reduce the amount of information but preserving the homological properties. In particular, thanks to discrete vector fields, we are able to compute, inside Coq, homological properties of biomedical images which otherwise are out of the reach of this system.