Photophysical image binarization.

Synthetic images of fluorescent beads were generated as described in Sec. S4 in S1 Text at different signal-to-noise ratios (with known values of λbg and λsig). For these images we know the ground truth pixel identity, i.e., which pixels are background and which are signal. (a) Estimated λbg compared to the ground truth value. (b-f) Our image binarization method was applied to the synthetic images (with binarization threshold pbinarize). The result was then compared to ground truth pixel identity, with success rates quantified through five statistical observables (blue). The orange marks correspond to our a priori prediction of the same observables (obtained without the knowledge of the ground truth). We also show Otsu’s method compared to ground truth pixel identities (red). In our method we have excellent control over the FPR, i.e., the fraction of white pixels in background regions. We also have good control over the FNR. Particularly important to notice is that our a priori prediction (orange) for all statistical observables agree very well with ground truths (blue). This agreement is the strength of our novel thresholding method, which hence opens up for unsupervised image thresholding where the error for the classification for each pixel is obtained a priori. The image count threshold for the binarization was determined through a p-value threshold pbinarize = 0.01.</p

Photophysical image segmentation.

(a) Beads image with detected regions (connected components of white pixels). The original image can be found in Fig 1a). The yellow pixels are boundary points to the detection regions. The binarized image used as input to our segmentation approach is found in S9 Fig (panel b) in S1 Text (b) Lung cell nuclei image with detected regions. The original image can be found in S7 Fig in S1 Text (a). Segmenting larger object with lower magnification is more challenging, since the background illumination will vary. We here tile the image and set p-value thresholds pGoF = 0.01 and pbinarize = 0.01 and region size gap threshold = 1. An example of the associated image count histogram with an overlaid fit is found in S7 Fig in S1 Text. Notice that our image segmentation method performs visually well on both experiments.</p

Estimates of the chip parameters for an EMCCD camera at different gain settings.

The calibration data shown in S1 Fig in S1 Text was used, and the chip parameters were calculated using Eqs (4)–(7) in Materials and Methods.</p

Estimating λ_<i>bg</i> for an image which contains both background and signal.

(a) Experimental fluorescence microscopy image of fluorescent beads. Here, the image is split into tiles of size 64x64 pixels, where each tile is given a label {row, column}, where in this example row, column = 1, …, 8. The contrast is set to better display the background noise and glass slide artifacts. (b) Estimating λbg: A histogram of the image counts for a single tile, here tile {4, 1}. The blue bars represent pixels regarded as true background, while the orange bars represent the outliers (not true background or signal pixels). The image counts threshold, , separating the blue and orange bars was determined using a p-value threshold, pGoF = 0.01, for the goodness-of-fit tests. The dashed black curve shows the fitted PMF for the estimated λbg, extended to the full range of image counts (in our method, we fit a truncated PMF to the blue bars). In S5 Fig in S1 Text, we provide the estimates of λbg and for all tiles in panel a). In S8 Fig in S1 Text, we also provide two more examples of image count histograms with overlaid fits. Examples of fits to histograms for synthetic images at varying SNR is found in Sec. S7 in S1 Text. A major novelty of our method is that we are able to estimate λbg for a arbitrary fluorescence image even though the image contains signal pixels.</p

Detailed description of our methods and supporting figures.

We here provide all necessary details of our PIA methods and supporting figures. (PDF)</p