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  • 1.
    Byttner, Wolf
    Linköping University, Department of Mathematics.
    Classifying RGB Images with multi-colour Persistent Homology2019Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
    Abstract [en]

    In Image Classification, pictures of the same type of object can have very different pixel values. Traditional norm-based metrics therefore fail to identify objectsin the same category. Topology is a branch of mathematics that deals with homeomorphic spaces, by discarding length. With topology, we can discover patterns in the image that are invariant to rotation, translation and warping.

    Persistent Homology is a new approach in Applied Topology that studies the presence of continuous regions and holes in an image. It has been used successfully for image segmentation and classification [12]. However, current approaches in image classification require a grayscale image to generate the persistence modules. This means information encoded in colour channels is lost.

    This thesis investigates whether the information in the red, green and blue colour channels of an RGB image hold additional information that could help algorithms classify pictures. We apply two recent methods, one by Adams [2] and the other by Hofer [25], on the CUB-200-2011 birds dataset [40] andfind that Hofer’s method produces significant results. Additionally, a modified method based on Hofer that uses the RGB colour channels produces significantly better results than the baseline, with over 48 % of images correctly classified, compared to 44 % and with a more significant improvement at lower resolutions.This indicates that colour channels do provide significant new information and generating one persistence module per colour channel is a viable approach to RGB image classification.

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