Advances in the application of computational topology

Analyzing the inner topological organization of epithelial tissue

In [1], we first used the concept of persistent entropy for the study of self-organization of cells. Some initial experiments were described, working on two types of tissues: chick neuroepithelium (cNT) from chicken embryos and wing imaginal disc in the prepupal stage (dWP) from Drosophila. In [2] (JCR Q1), weproved that persistent entropy is robust to noise, that is, small perturbation in the input data leads to a “controlled” change in the computed value of persistent entropy, supporting the idea that the algorithms based on persistent entropy are robust. Later, in [3], we performed an experiment involving three types of epithelial tissues (which have convex-like cells): cNT, dWP and middle third instar wing discs, dWL. The tissues dWP and dWL are two proliferative stages searated by 24h development (and hence, with very similar organization). We constructed alpha-complexes out of the centroids of the segmented cells. Then, we computed their persistent homology and persistent entropy. The statistical analysis of the resulting entropy values confirmed the differences between the three types. Parallel to these initial works, we have also collaborated with the biopharmaceutical research company Celgene interested in the applications of topology to the analysis of colonies of stem cells [4].

Objectives

Our main goal in this research line is to characterize differentcell arrangements in epithelial tissues using their topological-geometrical distribution. Specific goals areas follows:

  1. Develop an algorithm for topological analysis of images segmented into regions. The procedure must be independent of the scale. Different topological summaries will be studied.
  2. Set the most general requirements that images segmented into regions need to satisfy to be a proper input of our algorithm.
  3. Fully understand the topological/geometrical properties of different topological summaries (number of bars, total bars length, norm of landscapes, persistent entropy) in the context of the self-organization of the regions in the image.
  4. Perform statistical tests to study the results of different topological summaries.
  5. Implement the designed algorithms, creating a free access library/package.
  6. Perform wide experimentation on both real biological tissue images and synthetic images simulating the cells (given by Voronoi regions).
  7. Generalize our method to analyze arrangements of regions partitioning a 3D space.

Emotion recognition through a topological-based computer-vision approach

In [5], a model based on topology was developed to obtain a single real value of each audio signal. These data were used as input of a vector support machine to classify audio signals into eight different emotions: neutral, calm, happy, sad, angry, fearful, disgust, and surprised. The results obtained were close to the existing accuracy for severalmethods with greater scope.

Objectives

The main goal of this research line is to develop an approach for emotion recognition combining topological features of the image and audio sequences in talking-face videos. The final goal will be a method that computes a topological signature for each input video for emotion recognition purposes. Specific goals areas follows:

  • Compute a 9-dimensional vector merging audio signal and image sequence from a video using topology-based tools such as persistent entropy.
  • Extract topological features from the high dimensional vector space obtained after computing the Taken’s embedding.
  • Compare both approaches.

    • References

    1. MJ Jiménez, M Rucco, P Vicente-Munuera, et al: Topological Data Analysis for Self-organization of Biological Tissues. IWCIA LNCS 10256: 229-242 (2017)
    2. N Atienza, R Gonzalez-Diaz, M Soriano-Trigueros. On the stability of persistent entropy and new summary functions for topological data analysis. Pattern Recog., 107: 107509 (2020)
    3. N Atienza, LM Escudero, MJ Jiménez, MSoriano-Trigueros. Characterizing epithelial tissues using persistent entropy. CTIC2019 LNCS 11382:179–190 (2019)
    4. MJ Jimenez. Segmentación de CFU en Imágenes de Ensayos de Colonias Mediante Técnicas de Análisis Espacial. Contrato 68/83: P028-19/E29. Celgene Research S.L.U(2019)
    5. R Gonzalez-Diaz, E Paluzo-Hidalgo, JF Quesada. Towards emotion recognition: A persistent entropy application. CTIC LNCS 11382: 96-109 (2019)