Fig 1.
Adaptive identification of subcellular structures in superresolution microscopy in tandem with belief based labelling of each object’s support for the cell level genotype. Each image can have a set of labels, SPECHT then computes for each identified object o the support it has per individual label.
Fig 2.
The negative Laplacian (A.3-V, B.1)) can be leveraged to detect Gaussian 2D observations of 3D fluorescent objects. Thresholding V is a balance between high precision (B.2) and high recall (B.3)
Fig 3.
Kurtosis based thresholding illustrated on two in silico images. A: N = 35, , B: N = 12,
, sources randomly placed, with isotropic PSF. A.2 and B.2 show the negative Laplacian, and illustrate how it is less susceptible to intensity differences. C.1: The intensity distribution of both images. C.2: The distribution of the Laplacian of both images. C.3: The automatically derived threshold based on kurtosis can be scaled in favor of precision (PRC < 1) or recall (PRC > 1). The plot shows how kurtosis space thresholding follows the different shapes of the distributions.
Fig 4.
Graphical illustration of the concept of plausibility, belief, and uncertainty in the context of belief theory and as used in the remainder of this manuscript. A.2: Plausibility and belief can be expressed as the complement of their respective support. A trivial, or naive, model has a plausibility of 1, belief 0, and uncertainty 1. A.3–6: Illustrates the flexibility of belief theory based modelling. Weak, but certain evidence (A.3) occurs when belief and plausibility are equal, yet small. Conversely strong evidence can be certain (A.5), but does not need to be (A.4). Finally, absence of quantifiable evidence is mapped to ‘ignorance’, maximal uncertainty, where belief is 0, plausibility1.
Table 1.
Dempster combination enabling the expression of a joint model. A, B, C ⊂ Θ.
Fig 5.
Consistency compared to existing methods.
We simulate 3 markedly different in silico scenarios where light sources are either dominated by bright, dim, or are a mixture of both. Note that SPECHT is not always optimal, but does produce consistent results across these variable conditions. Green marks true positives, the location of the actual objects. Red marks false positives, predicted objects that do not exist. Blue circles denote false negatives, objects that should be detected, but are not.
Fig 6.
SNR decreases rapidly as the parameters of both noise sources (Gaussian, Poisson) are increased, yet SPECHT’s recovery of faint objects remains stable under moderate noise conditions. At severe noise levels, as is expected, artifacts appear, while sources with intensity lower than background intensity can no longer be recovered. Green marks true positives, the location of the actual objects. Red marks false positives, predicted objects that do not exist. Blue circles denote false negatives, objects that should be detected, but are not.
Fig 7.
Robustness on partially annotated STED images.
We illustrate how the belief stage of SPECHT complements the object detection stage on real world STED microscopy images (A.I-III), subsequently degraded with severe noise (C). We first run SPECHT in high recall mode on selected ROIs of a PC3-CAVIN1 cell, where an expert makes partial annotation (B-white box) of structures of interest. The belief stage then uses a single CAV1 KO cell to learn which identified objects are non-specific labelling (red), versus actual objects of interest (green), on a continuous scale. Next, we repeat the experiment but severely degrade the image with added Poisson and Gaussian noise. The reduced signal to noise ratio induces more artifacts, but the belief stage identifies these as non-specific labelling with high plausibility. Scale bar (A.I) = 120nm
Fig 8.
Visualization of results on CAV1 datasets.
A: Object detection results on the 3 cell lines with a markedly different intensity profile. B.1: A Venn diagram illustrating how we differentiate between different genotypes. B.2 SPECHT labelling function assigns each object 3 values representing the belief that the object is evidence for either of the 3 object types. C: Illustration of the results on a PC3-CAVIN1 cell. C.3-a, c, d are identified as caveolae with high likelihood, C.3-b as scaffold, C.3-e as background.
Fig 9.
A: Validation with respect to previous art (A.1) and biological ground truth (A.2). A: The distribution of SPECHT’s label (A.1, x-axis: P[object] = caveolae) shows a distinct long left tail, containing 20% of the data. The frequency division matches previous art in dSTORM analysis. Caveolae only form in the presence of CAVIN1, therefore the probability of an object being Caveolae should correlate with the colocalization of CAVIN1 (A.2), which is what we observe. B.1: The detection threshold (∼0.35, A.1–2) matches the sudden rise in colocalization when we use a LOWESS regression, rather than a linear regression, and results are consistent across 3 replications (30 cells total, each line represents a single cell). B.2: Varying hyperparameters does not alter the consistency of the result with respect to biological ground truth (colocalization CAVIN1). The dotted line corresponds to the frequency (20%) of Caveolae detected in dSTORM using network analysis.
Fig 10.
A: Belief calculus enables the combination of models learned data originating from different microscopes. B: We visualize how the joint model operates on a single image of retinal tissue stained for amyloid-β, sourced from an AD+ positive patient. Object marked in red express a high belief in being AD+ specific. C: We offer the end user a per-object expression of the conflict between the 2 models that create the joint model. An increased weight of conflict (Y-axis) indicates the models disagree on the labelling for a specific object. We illustrate the visualization here for 3 AD+ images. Observe that for objects where both models are uncertain (∼.5) their minimal conflict is higher than it is for objects that have a higher support for being either AD+ specific or healthy.