Limits...
Graphical methods for quantifying macromolecules through bright field imaging.

Chang H, DeFilippis RA, Tlsty TD, Parvin B - Bioinformatics (2008)

Bottom Line: In rare cases where nuclear signal is significantly altered as a result of sample preparation, nuclear segmentation can be validated and corrected.Finally, segmented stained patterns are associated with each nuclear region following region-based tessellation.Compared to classical non-negative matrix factorization, proposed method: (i) improves color decomposition, (ii) has a better noise immunity, (iii) is more invariant to initial conditions and (iv) has a superior computing performance.

View Article: PubMed Central - PubMed

Affiliation: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. hchang@lbl.gov

ABSTRACT
Bright field imaging of biological samples stained with antibodies and/or special stains provides a rapid protocol for visualizing various macromolecules. However, this method of sample staining and imaging is rarely employed for direct quantitative analysis due to variations in sample fixations, ambiguities introduced by color composition and the limited dynamic range of imaging instruments. We demonstrate that, through the decomposition of color signals, staining can be scored on a cell-by-cell basis. We have applied our method to fibroblasts grown from histologically normal breast tissue biopsies obtained from two distinct populations. Initially, nuclear regions are segmented through conversion of color images into gray scale, and detection of dark elliptic features. Subsequently, the strength of staining is quantified by a color decomposition model that is optimized by a graph cut algorithm. In rare cases where nuclear signal is significantly altered as a result of sample preparation, nuclear segmentation can be validated and corrected. Finally, segmented stained patterns are associated with each nuclear region following region-based tessellation. Compared to classical non-negative matrix factorization, proposed method: (i) improves color decomposition, (ii) has a better noise immunity, (iii) is more invariant to initial conditions and (iv) has a superior computing performance.

Show MeSH
An example of two-terminal (class) graph-cut segmentation: (a) an image grid (3 × 3), where ‘F’ and ‘B’ correspond to foreground and background seeds, respectively; (b) a graph constructed from image (a); (c) an optimum cut shown as a red line; and (d) a final labeling result where grid points are assigned to terminals S and T after the cut.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2666809&req=5

Figure 3: An example of two-terminal (class) graph-cut segmentation: (a) an image grid (3 × 3), where ‘F’ and ‘B’ correspond to foreground and background seeds, respectively; (b) a graph constructed from image (a); (c) an optimum cut shown as a red line; and (d) a final labeling result where grid points are assigned to terminals S and T after the cut.

Mentions: Signal decomposition, through color unmixing, aims to identify the signaling macromolecules that are associated with each dye. For example, Figure 2 shows how labels for nuclei and lipids are distributed in the RGB space. The main contribution of this article is in characterizing color unmixing as a segmentation problem that incorporates neighborhood information through a global optimization framework. The optimization framework is based on the graph-cut method (Boykov and Marie-Pierre, 2001), which is briefly summarized. In this context, the image is represented as a graph , where is the set of all nodes, and Ē is the set of all arcs connecting adjacent nodes. Usually, nodes and edges correspond to pixels (𝒫) and their adjacency relationship, respectively. Additionally, there are special nodes that are known as terminals, which correspond to the set of labels that can be assigned to pixels. In the case of a graph with two terminals, terminals are referred to as the source (S) and the sink (T). The labeling problem is to assign an unique label xp (0 for background, and 1 for foreground) for each node , and the image cutout is performed by minimizing the Gibbs energy E (Geman and Geman, 1984):(8)where E1(xp) is the likelihood energy, encoding the data fitness cost for assigning xp to p, and E2(xp, xq) is the prior energy, denoting the cost when the labels of adjacent nodes, p and q, are xp and xq, respectively. The likelihood energy is computed in an eight-connected neighborhood. Figure 3 shows how a local neighborhood is partitioned through a two-terminal graph-cut segmentation.Fig. 3.


Graphical methods for quantifying macromolecules through bright field imaging.

Chang H, DeFilippis RA, Tlsty TD, Parvin B - Bioinformatics (2008)

An example of two-terminal (class) graph-cut segmentation: (a) an image grid (3 × 3), where ‘F’ and ‘B’ correspond to foreground and background seeds, respectively; (b) a graph constructed from image (a); (c) an optimum cut shown as a red line; and (d) a final labeling result where grid points are assigned to terminals S and T after the cut.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2666809&req=5

Figure 3: An example of two-terminal (class) graph-cut segmentation: (a) an image grid (3 × 3), where ‘F’ and ‘B’ correspond to foreground and background seeds, respectively; (b) a graph constructed from image (a); (c) an optimum cut shown as a red line; and (d) a final labeling result where grid points are assigned to terminals S and T after the cut.
Mentions: Signal decomposition, through color unmixing, aims to identify the signaling macromolecules that are associated with each dye. For example, Figure 2 shows how labels for nuclei and lipids are distributed in the RGB space. The main contribution of this article is in characterizing color unmixing as a segmentation problem that incorporates neighborhood information through a global optimization framework. The optimization framework is based on the graph-cut method (Boykov and Marie-Pierre, 2001), which is briefly summarized. In this context, the image is represented as a graph , where is the set of all nodes, and Ē is the set of all arcs connecting adjacent nodes. Usually, nodes and edges correspond to pixels (𝒫) and their adjacency relationship, respectively. Additionally, there are special nodes that are known as terminals, which correspond to the set of labels that can be assigned to pixels. In the case of a graph with two terminals, terminals are referred to as the source (S) and the sink (T). The labeling problem is to assign an unique label xp (0 for background, and 1 for foreground) for each node , and the image cutout is performed by minimizing the Gibbs energy E (Geman and Geman, 1984):(8)where E1(xp) is the likelihood energy, encoding the data fitness cost for assigning xp to p, and E2(xp, xq) is the prior energy, denoting the cost when the labels of adjacent nodes, p and q, are xp and xq, respectively. The likelihood energy is computed in an eight-connected neighborhood. Figure 3 shows how a local neighborhood is partitioned through a two-terminal graph-cut segmentation.Fig. 3.

Bottom Line: In rare cases where nuclear signal is significantly altered as a result of sample preparation, nuclear segmentation can be validated and corrected.Finally, segmented stained patterns are associated with each nuclear region following region-based tessellation.Compared to classical non-negative matrix factorization, proposed method: (i) improves color decomposition, (ii) has a better noise immunity, (iii) is more invariant to initial conditions and (iv) has a superior computing performance.

View Article: PubMed Central - PubMed

Affiliation: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. hchang@lbl.gov

ABSTRACT
Bright field imaging of biological samples stained with antibodies and/or special stains provides a rapid protocol for visualizing various macromolecules. However, this method of sample staining and imaging is rarely employed for direct quantitative analysis due to variations in sample fixations, ambiguities introduced by color composition and the limited dynamic range of imaging instruments. We demonstrate that, through the decomposition of color signals, staining can be scored on a cell-by-cell basis. We have applied our method to fibroblasts grown from histologically normal breast tissue biopsies obtained from two distinct populations. Initially, nuclear regions are segmented through conversion of color images into gray scale, and detection of dark elliptic features. Subsequently, the strength of staining is quantified by a color decomposition model that is optimized by a graph cut algorithm. In rare cases where nuclear signal is significantly altered as a result of sample preparation, nuclear segmentation can be validated and corrected. Finally, segmented stained patterns are associated with each nuclear region following region-based tessellation. Compared to classical non-negative matrix factorization, proposed method: (i) improves color decomposition, (ii) has a better noise immunity, (iii) is more invariant to initial conditions and (iv) has a superior computing performance.

Show MeSH