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Lists with This Book. This book is not yet featured on Listopia. Community Reviews. Showing Rating details. All Languages. More filters. Sort order. Perry rated it it was amazing Dec 14, Bill marked it as to-read Feb 01, Alex marked it as to-read Dec 23, Bria added it Mar 07, Among the various methods, the outline PCA method achieves the best reconstruction performance.

Modeling 2D shapes is generally easy and even simple methods can achieve desirable performance, but this is much less true for 3D shapes. As mentioned before, usually shapes are parameterized as features that capture shape variance. The parameterization is very important and frequently determines the accuracy of models. Before comparing different methods for modeling 3D shapes, we first focused on how the parameterization approach affected performance of one of those methods, SPHARM descriptors. Illustrations of HeLa 3D parameterization reconstruction with different methods.

Form and Transformation Generative and Relational Principles in Biology

Three cells are randomly picked with the reconstructions for different methods for the same cell in a row. None of the existing methods worked well for all kinds of cell shapes, whether round cell shapes or complex cell shapes with neurites. As described in the Methods, these included improvements in the surface preparation, initial parameterization and optimization. A parameterization is considered failed if the reconstruction error for the original descriptor is greater than pixels.

The right side shows the average convergence times. Once shape parameterizations descriptors were obtained, PCA was used to project the parameterization to a low dimensional latent space as SCA is a variant of PCA and we found it did not provide significant improvement, we did not include it in further comparisons. For comparison, auteoncoders were used to directly perform dimension reduction from images.

For some other spherical harmonic based methods i. Note : Same as 2D datasets, we only show the results for 7 dimensions for HeLa 3D dataset for diffeomorphic model. In the parenthesis, we show the reconstruction errors after filtering out isolated voxels in the reconstruction. For all methods, similar to our findings for 2D, we observe that low dimensional encodings can only reconstruct smooth shapes.

As the dimension increases, more shape variance can be captured. However, even in high dimensional space, AE are not able to capture fine shape variances. The cells are chosen based on the quantiles of reconstruction errors in latent dimension , which are listed in the left side.

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The reconstructions of different latent dimensions are shown with same cell in the same row, along with the ground truth. An important application of shape space methods is to model shape evolution. This is relevant to studying cell dynamics, e. Neuron differentiation from an approximately round cell to a neuron with neurites is a particular example. As described in the Methods section, interpolation in the shape space can be applied to find intermediate shapes between source and target shapes.

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The results are especially noteworthy for SNL 3D shapes, in that it simulates a process of neurite growth, even though no knowledge of how a neurite grows is used in the model. Illustrations of shape evolutions for SNL 3D dataset. Four pairs of cells are randomly selected. The source, target and intermediate shapes in the linear path are shown, with the title showing the distance to the source.

The source and target are labeled as 0 and 1. These simulations assume that no information is available about the likely changes that might occur between two specific shapes or even if they are likely to occur at all. In this case, a reasonable assumption is that the evolution between two shapes takes place along a path that minimizes the total difference between the intermediate shapes and the starting and ending shape.


Depending on the method used for shape space construction, finding this path is typically quite expensive. In diffeomorphic methods, extensive computation is done to find the minimum energy path, and hence the distance, between all pairs of shapes before the shape space is constructed, and synthesizing along this path is therefore inexpensive. In other methods that are faster, the minimal energy path would need to be found by search after the construction of the shape space.

Thus, minimum energy evolution is expensive either way especially in high dimensions. As a practical consideration, we therefore investigated whether simply interpolating along a linear path would give a reasonably low energy. For each method, the evolution energy is smaller when the latent dimension is high, consistent with our previous observation that intermediate shapes in higher dimensions are more like the source and target shapes. The normalized energies by the Hausdorff distance between the source and target are shown in the table the optimal value is 0.

Smaller energies mean more efficient transformations. The relationship between cell and nuclear shape is also an important aspect that may be involved in cellular processes. Previous work has shown that there are dependency relationship between the two Johnson et al. We therefore next evaluated the performance of various methods on the task of modeling both cell and nuclear shape.

One potential criterion for reconstruction error for joint modeling is to apply Hausdorff distance for both cell and nuclear shapes, however, in this case, the errors for nuclear shapes will be missed because of the dominance of cell shape errors. Therefore, we calculated the reconstruction errors for cell and nuclear shapes separately and averaged them as the joint error. As seen in the tables, for each method, the differences of the reconstruction accuracy for joint modeling and separate modeling are small for the same method in the same latent dimension.

Again among all methods, outline PCA for 2D and our method for 3D have the best performances either with joint or separate modeling. As shown in Supplementary Tables S2 and S3 , for outline PCA methods, joint model errors for cell shape decrease while the errors for nuclear shape increase, compared with the separate models, indicating that greater overall weight was put on the cell shape in the joint models. However, here we should stress that the success of separate modeling does not imply that there is no relationship between the two components that relationship is captured by explicit features.

It simply means that there is no advantage to taking that relationship into account when learning the component shape models themselves. Illustrations of joint modeling of cell and nuclear shapes for different methods for CYTO dataset. Here we choose a cell in the quantile of 0. The original shape is shown in black and the reconstruction is shown in red.

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  8. This cell is shown across different methods and different latent dimensions, which are indicated in the title and the Y-axis, respectively. Note : The table shows two latent dimensions 14 and for the four 2D datasets for four representative methods. Note : The errors for the three representative methods with dimensions 14 and are shown.

    For 2D cell shapes, in low dimensional space, all of these methods reconstruct overly-smooth shapes that are not realistic. When increasing latent dimension, these methods can all achieve better reconstruction performances, however, deep autoencoders are not as good as outline PCA and SCA methods, which can well preserve local variance and thus reconstruct shapes nearly perfectly.

    Our method improves the robustness of the mapping of the original cell shape to a sphere, and works well even for highly non-spherical shapes.

    Bio-objects and generative relations

    Deep learning methods typically require a lot more computing resources and more training data of course, deep learning methods are continuously evolving and this may change. However, our results do not necessarily mean that other methods are inferior in all aspects of cell analysis. As shown previously, diffeomorphic models work well for mapping protein distributions inside cells Roybal et al. In addition, supervised deep learning methods often significantly outperform traditional methods for classification tasks in which detailed cell shape information may not be needed.

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    Thus, careful consideration should be given based on the specific task when working with cell images. In the absence of any additional information, however, they represent the best prediction that can be made. When available, movies can be used to calculate vector fields in the shape space that may give more accurate cell shape changes Johnson et al.

    Even so, they can only be accurate up to the temporal resolution of the movies. We have focused here on the task of accurate cell and nuclear shape reconstruction from models.