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Shape, Appearance and Spatial Relationships

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Guide to Medical Image Analysis

Part of the book series: Advances in Computer Vision and Pattern Recognition ((ACVPR))

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Abstract

Object detection in medical image analysis can be modelled as a search for an object model in the image. The model describes attributes such as shape and appearance of the object. The search consists of fitting instances of the model to the data. A quality-of-fit measure determines whether one or several objects have been found. Generating the model for a structure of interest can be difficult. It has to include knowledge about acceptable variation of attributes within an object class while remaining suitably discriminative. Several techniques to generate and use object models will be presented in this chapter. Information about acceptable object variation in these models is either generated from training or is introduced via modeling. In either case, an efficient representation is needed with (relatively) few parameters yet being able to represent variation of shape and appearance between subjects. Applying shape (and appearance) models to the data may produce the object segmentation or they may be used as additional constraint in a subsequent segmentation process. This chapter closes with a discussion on how shape models can be used to augment data-driven segmentation by a shape model component.

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Notes

  1. 1.

    The notation is the usual shorthand notation for HOM operators combining the two structuring elements in a single operator. The ‘0’s represent the erosion structuring element that is applied to the inverted binary image and the ‘1’s represent the erosion structuring element that is applied to the original binary image.

  2. 2.

    A rule of thumb borrowed from statistical pattern recognition for estimating likelihood functions from samples predict for a 100-dimensional feature space that at least 2100 samples would be needed.

  3. 3.

    Each of the models presented here can be essentially extended such that it can replace any of the other models. However, each of the models has been built with some idea about the objects to be described and the way necessary knowledge is to be gathered. It works most efficiently if objects or scenes to which it is applied follow this idea.

  4. 4.

    A FEM may be defined in a similar fashion than the mass-spring model by letting 1d springs being the elements. In such case, a bounded 2d or 3d object may be represented by a dense mesh of springs restricting shape variation.

  5. 5.

    Node values and force values of all nodes of an element (and later of the complete FEM mesh) are combined in a single vector. Hence, values for a node with index i in 2-d have indices 2i and 2i + 1 in the displacement vector u and the external force vector f.

  6. 6.

    This kind of assemblage becomes costly for the sparse matrix K if N is large. Faster methods to carry out this operation exist but the operation itself stays the same. For application in medical image analysis, however, the size of N is usually small (i.e., N ≪ 100.000) and model creation does not happen often.

  7. 7.

    A dynamic system can be modeled without damping but damping prevents oscillation.

  8. 8.

    These modes are not contained in an ASM, since influence from rotation and translation is removed during normalization of the training data.

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  1. Computer Science Department, ISG, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Klaus D. Toennies

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Toennies, K.D. (2017). Shape, Appearance and Spatial Relationships. In: Guide to Medical Image Analysis. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-7320-5_11

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