Processing chromatic information in histological data  

*Nektarios Valous (Applied Tumor Immunity Clinical Cooperation Unit, National Center for Tumor Diseases (NCT), German Cancer Research Center (DKFZ), Im Neuenheimer Feld 460, 69120, Heidelberg, Germany)
Rodrigo Rojas Moraleda (Applied Tumor Immunity Clinical Cooperation Unit, National Center for Tumor Diseases (NCT), German Cancer Research Center (DKFZ), Im Neuenheimer Feld 460, 69120, Heidelberg, Germany)
Eckhard Hitzer (College of Liberal Arts, International Christian University, Osawa 3-10-2, 181-8585 Mitaka, Tokyo, Japan)
Dragoş Duşe (Department of Medical Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital, Im Neuenheimer Feld 460, 69120, Heidelberg, Germany)
Meggy Suarez-Carmona (Department of Translational Immunotherapy, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120, Heidelberg, Germany)
Anna Berthel (Department of Medical Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital, Im Neuenheimer Feld 460, 69120, Heidelberg, Germany)
Dirk Jäger (Department of Medical Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital, Im Neuenheimer Feld 460, 69120, Heidelberg, Germany)
Inka Zörnig (Department of Medical Oncology, National Center for Tumor Diseases (NCT), Heidelberg University Hospital, Im Neuenheimer Feld 460, 69120, Heidelberg, Germany)
Niels Halama (Department of Translational Immunotherapy, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, 69120, Heidelberg, Germany)

Whole-slide imaging of histological sections enables the detailed spatial interrogation of the entire tissue landscape in expansive high-resolution images containing billions of pixels. The intensity and distribution of the chromogen information in histological stains at specific locations of interest provides clinically important information regarding disease diagnosis and prognosis. The proposed approach is based on a simple, rapid, and flexible method of digitally visualizing and separating staining information using quaternion algebra. By conveniently rewriting the quaternionic representation of histological images with simple algebraic operations, it is feasible to decompose them into different spectral representations that can visualize and separate the contextual chromatic information. This pixel-based approach is computationally efficient thus taking advantage of parallel architectures in computing systems. The benefits of the proposed approach for medical images can be translated as a means for optimized manual assessments by clinicians, and as a key step of digitally separating chromatic regions of interest for further quantification in automated processing pipelines.

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