Nonnegative Mixed-Norm Convex Optimization for Mitotic Cell Detection in Phase Contrast Microscopy

This paper proposes a nonnegative mix-norm convex optimization method for mitotic cell detection. First, we apply an imaging model-based microscopy image segmentation method that exploits phase contrast optics to extract mitotic candidates in the input images. Then, a convex objective function regularized by mix-norm with nonnegative constraint is proposed to induce sparsity and consistence for discriminative representation of deformable objects in a sparse representation scheme. At last, a Support Vector Machine classifier is utilized for mitotic cell modeling and detection. This method can overcome the difficulty in feature formulation for deformable objects and is independent of tracking or temporal inference model. The comparison experiments demonstrate that the proposed method can produce competing results with the state-of-the-art methods. 1. Introduction Measurement of the proliferative behaviors of cells in vitro is important to many biomedical applications, such as drug discovery, stem cell manufacturing, and tissue engineering. Recently, the need for extended-time observation and the proliferation of high-throughput imaging have made automatic mitotic cell detection mandatory. The state-of-the-art methods for this task generally fall into two categories. (1)？ ？Spatial feature-based method: this kind of methods detects mitotic cells directly in an image depending on spatial visual characteristics. Liu et al. [1] considered mitotic cell as a special visual pattern and train a Support Vector Machine classifier with region features for identification. Li et al. [2] extracted volumetric Haar-like features and implemented a cascade framework to classify spatiotemporal sliding windows of an image sequence. Since the current low level visual features usually have low discrimination for nonrigid and deformable objects, this kind of methods always achieves unsatisfactory performances. (2) ？？Sequential feature-based method: this kind of methods usually implement object tracking or temporal inference models to leverage sequential features for decision. Yang et al. [3] extracted individual cell trajectories by cell tracking and identified mitoses with the dynamic features of the mother and daughter cells during mitosis progression. To handle the difficulty by cell tracking, temporal inference models are implemented to leverage the temporal context for mitosis event recognition. Gallardo et al. [4] trained a hidden Markov model for mitosis recognition with cell shape and appearance dynamics. Liu et al. [5] applied a hidden-state conditional random field to