Fig 1.
Phase contrast causes an intensity gradient at the location of the RBC membrane.
(A) Bright-field image of a RBC. (B) Intensity profile along the black line in (A). The vertical line indicates the contour-position as found with the method described in [13]. The background intensity and fit are also indicated (horizontal and diagonal line). (C) Intensity-gradient of (B). The vertical line indicates the maximum. The noise in the image cause two maxima at the peak, which makes localizing the absolute peak value difficult without filtering.
Table 1.
Parameter values used for imaging and tracking RBCs.
Fig 2.
The new algorithm uses oversampling of the intensity gradient to determine the membrane position with sub-pixel precision.
(A) Illustration of the local angles φj and their position on the halo. (B) Determination of local coordinate pj in a given direction φj. The fit is performed between the intensity minimum and maximum indicated by the arrows. This corresponds to Method 1 explained in the text. Note that the fit position (horizontal arrow) lies in-between the positions and intensity values of the individual pixels (black squares). This is made possible by the linear interpolation. The background intensity is determined just outside the halo. (C) Fit slopes as a function of the local angle. The maximum is perpendicular to the halo.
Fig 3.
Flow-chart of the segmentation algorithm illustrating the steps that are taken in processing the movie.
The section indicated by the red rectangle indicates the embarrassingly parallel part of the algorithm, which can easily be adapted for parallel processing on a GPU.
Fig 4.
Examples of microscopic objects that have successfully been tracked using our new segmentation algorithm.
The obtained contour is indicated by the black line that is overlaid on each image. All images were recorded with bright-field light-microscopy, except for the E. coli, which was recorded using a phase-contrast objective (100x, NA1.45).
Fig 5.
Image pixilation causes jitter in the positions obtained with the classical algorithm.
(A) Illustration of how fitting at an offset from the gradient maximum affects the obtained fit-slope and results in a deviation in the final coordinate. (B) Comparison of the reference contour and the contour coordinates obtained from the previous method [13], and our refined algorithm here described. The artifact described in (A) leads to transverse shifts in the final position (black squares), whenever the pixel-position about which the fit is performed (dashed line) shifts transversely to the contour. The red line represents reference position of the circle used in the synthesis of the image with SNR = ∞, which is shown in the inset indicating the shown area with a white rectangle. The tracked coordinates obtained from the new algorithm (white diamonds) follow the reference position precisely.
Fig 6.
Comparison of the radius fluctuation time-series obtained from a measurement of a POPC GUV using Pécréaux’ algorithm (A) and our algorithm (B). The artifacts from imprecise fitting leads to various maxima in the displacement-distributions spaced 1px apart. This artifact is not present when using our new method.
Fig 7.
Segmentation precision depends on image noise and the slope of the intensity gradient.
(A) Segmentation precision δ1σ versus 1/SNR for a dried RBC at different exposure times (‘*’) and for three synthetic datasets (‘□,○ and Δ’) with different level of contrasts/slopes m. The precision values from each dataset fall onto a straight determined by the contrast/slope m. (B) After renormalizing x-axis to σi/m all values fall onto a straight y = 0.54 ∙ x allowing for easy estimation of the segmentation precision from the two known quantities σi and m. Note that the contrast/slope values are for to unit background intensity.
Table 2.
Values for the dried RBC datasets compared to RBCs and GUVs in buffer solution.
Fig 8.
Comparison of spectra obtained from the same dataset (SNR = 106.7) using the new and old algorithm.
The spectrum from the old algorithm increase at high q, since the pixilation artifact causes increased noise as the wavelength draws closer to the pixel-size. The spectrum from the new algorithm exhibits a minimum at the location corresponding to wavenumber qpix of a pixel.
Fig 9.
Shape and level of the noise floor depends on the pixel size and SNR.
(A) Illustration of the inverse scaling behavior of the spectrum with pixel size. 1 × px corresponds to the experimental pixel size. The shape of the noise floor is the result of the pixel-noise being convoluted with kernel from the linear interpolation. (B) Plot of the spectra obtained for different SNRs. The noise floor decreases for higher (better) SNRs. At high SNRs (SNR ≥ 104) it begins to enter the noise due to numeric imprecision. Since this noise is independent of pixels, spectrum for SNR = ∞ is flat (red line).
Fig 10.
Example flicker spectra of GUV and RBC datasets obtained with the classical and new segmentation algorithms.
Top panels: Instantaneous snapshot of a fluctuating GUV made of POPC (A) a healthy RBC undergoing flicker motions (B). The microscopy images are taken with a CMOS camera in the PhC mode at the equatorial plane of the quasi-spherical objects (see Methods for details), and correspond to one frame taken arbitrarily in a movie recorded at 6kfps. Lower panels: Fourier space fluctuation spectra obtained from the statistical analysis of the membrane contour fluctuations. Results from the proposed new contour-segmentation algorithm are compared with results from the classical algorithm described in [13]. The pixelation form-factor, as empirically obtained from optically equivalent synthetic contours (non-fluctuating but including similar noise than the CMOS camera), are plotted as dashed lines with the characteristic sinc-like shape of a squared pixel grid. These lines represent the minimal floor noise corresponding to the instrumental “fluctuations” due to the electronic noise of the CMOS camera implemented with the current optical configuration. The wavenumber corresponding to a distance of one-pixel in Fourier space is plotted as a vertical dotted line labelled qpx = 2π/px.