Performance comparison of the proposed method and its variants.

<p>Grand average scores of (Blue) sensitivity, (Red) precision, and (Green) F-measure, obtained by the proposed methods and its variants. Note that three metrics are averaged over temporal and parametric axes, where the temporal axis includes 101 sequential images, while the parametric axis includes ten different sets of filtering parameters.</p

Summary of comparative performances based on F-measure metric.

<p>Initial lengths for the enhancement filtering (, , ) are varied in the range: () for single-scale, and (; ) for multiscale filtering. Intermediate values for each parameter are obtained by linear sampling at an interval of 5, i.e., at . All parameters are in pixel unit.</p

Contrast-enhanced 2D slices from our image dataset.

<p>Sample images with time-point and z-slice pairs at (A) (t25, 18), (B) (t34, 35), (C) (t45, 22), (D) (t86, 22), (E) (t91, 24), and (F) (t98, 29). Each image has dimension: 103 103 pixels and has voxel resolution: and µm.</p

Performance comparison using F-measure.

<p>F-measure values, obtained by (A) the proposed, (B) Variant-1, (C) Variant-2, and (D) Variant-3 over time. Results include 101 3D sequential images from a developing embryo containing 8 to 32 cells.</p

Summary of comparative performances based on F-measure metric.

<p>Initial lengths for the enhancement filtering (, , ) are varied in the range: () for single-scale, and (; ) for multiscale filtering. Intermediate values for each parameter are obtained by linear sampling at an interval of 5, i.e., at . All parameters are in pixel unit.</p

Estimated nuclei by the proposed method.

<p>Number of estimated nuclei for (A) embryo-1, (B) embryo-2, (C) embryo-3, and (D) embryo-4, respectively. Each embryo sequence consists of 271 images, i.e., s1 to s271, which contain nuclei from 2 to approximately 32 cell-stages.</p

Nuclei detection results for the proposed method and its variants.

<p>Number of extracted nuclei by (A) the proposed, (B) Variant-1, (c) Variant-2, and (D) Variant-3 over time. Results include 101 sequential images from a developing embryo containing 8 to 32 cells.</p

Robustness against high-valued parameters.

<p>(A) The number of estimated nuclei and the scores of (B) precision, and (C) sensitivity, and (D) F-measure over time, when arbitrarily large parameter values (e.g., (50, 62) pixels for multiscale, and 50 pixels for single-scale) are selected.</p

Robustness analysis against additive white Gaussian noise.

<p>(blue) SNR levels, (light-blue) ground truth, and the number of estimated nuclei for (red) the proposed, (green) previous-1, (purple) previous-2 against increasing noise spreads, when large initial parameters (, , and ) are selected. Note that the proposed method re-estimates a new set of parameters: , , and using feedback mechanism, while previous methods fail to do. A 3D image having 32 nuclei is considered for analysis.</p

Nuclei tracking results at 8- and 16-cell stages of an embryo.

<p>Nuclear motion tracks in the (A, B, C) 8-cell and (D, E, F) 16-cell stages; Blue and red lines in the 2D projected space (A, D) and 3D space (B, E) indicate the estimated and ground truth nuclear tracks without explicit moving directions; Color gradients in the 3D space (C, F) indicate the directions through which cells move inside the embryo. Blue and red colors indicate the start and end points of the moving cells. Note that twenty two frames (i.e., t1 to t22) at the 8-cell stage and twenty six frames (i.e., t36 to t61) at 16-cell stage are used for track generation. The selected distance threshold () for the correspondence establishment was 25 pixels.</p