Background removal by highpass filtering

 

Problem: You want to perform fluorescence intensity measurement, but the objects of interests appear on an inhomogeneous, uneven background.

Typical cases:

·         Cells at low magnification over a background fluorescence from the medium or excitation bleed through. This results in a brighter background in the center of the image than the sides.

·         Organelles (e.g. mitochondria) at high magnification, but the targeting of the fluorophore is inefficient and there is a background haze from the cytosol.

Solution: adaptive, local background subtraction.

 

Introduction:

Smaller, punctate and filamentous details are represented at high spatial frequencies (w) in Fourier domain, while the bulkier background at low spatial frequencies. Using these principles, the mitochondrial fluorescence of a calcium probe with imperfect mitochondrion selectivity was separated from the fluorescence of the probe localized in the cytosol with high pass filtering¹. In general, this technique works as local background removal².

 

Protocol:

Setting up the method: The aim is to determine the optimal filter function characteristics. This is typically performed for the specific size of object and magnification.

 

A)    Subjective / empirical method: if the purpose of the filtering is visualization of objects which are otherwise unseen due to the local background, then the aim is to find the highpass filter cut on frequency, where the desired details are well visible.

 

1.      With an image open, click Tools/Setup DFT Filter

2.      In the Setup DFT Filter and Filter Optimizations Dialog in the Calibration tab set the spatial resolution of the image, if w is intended to be used as cycles/mm. The spatial calibration is automatically filled from the image metadata if available. If w is used in pixels, this calibration value is indifferent.

3.      In the Generate tab and select filter function: 2D DFT Butterworth BP filter

4.      Set the cut on w value. w is a smaller value than 1/(2d) for d diameter objects when w is given in cycles/mm and d is in mm. When w is given in pixels a smaller value e.g. 3 is useful for general background removal, and ~10-20 for transmission of small objects, like mitochondria or protein aggregates (at 512´512 images).

5.      Set the order of cut on. Values 1-1.5 typically result minimal ring formation

6.      Set the cut off w value. If intending to use a highpass filter set a large number, e.g. 1000. If intending to do bandpass filtering set a larger number than the cut on w,  but smaller than the half size of the image in pixels or the ‘Maximal w‘ indicated in the Calibration tab

7.      The remaining parameters are discussed here: 2D DFT Butterworth BP filter

8.      Click the Generate button in the bottom. The filter coefficient graph is updated now on the left

9.      Click Preview.

10.  If background was not sufficiently eliminated, increase cut on w. If the details of interest are not transmitted, thinned or distorted lower values cut on w.

11.  If the preview image looks blurry increase the cut off w.

12.  If the preview image looks ringed decrease the order of the cut on. The order has to be at least 1.

13.  When the preview image is visually satisfying press Process or store values using the Set as Default button. In the latter case selecting the 2D DFT Butterworth BP filter from the Main menu will contain the optimized parameters.

14.  Alternatively the filter function can be saved. In this case the actual filter coefficients are stored. Saved filter functions can be loaded by the 2D DFT Filter function, or by the spatial filtering function of the Multi-Dimensional Open dialog.

 

B)    Objective method: If the purpose of the filtering is selective transmission of a signal originating from the mitochondrial compartment, calculation of filtered signals (e.g. comparison of signals over the mitochondria and the cytosol / nucleus¹ and the iterative modification or optimization of the filter function is may be required. This function is not yet migrated to the Image Analyst MKII.

 

Perform filtering:

1.      With an image open, click Filters/2D DFT Butterworth BP filter or Filters/2D DFT Filter in the main menu

2.     Set the parameters optimized above (alternatively use the function from the Pipeline, where parameters can be saved with the functions)

3.      Process image (by selecting image on the parameter bar as ‘Image A’ and pressing Process or by right clicking the image and using the Process this menu point.

4.      In order to make intensity measurements on the filtered image, the absolute value of the pixels has to be taken, or the negative pixel values have to be removed (details why). Set the Absolute parameter of the 2D DFT filter True. Alternatively, set all negative pixels to zero by using the Threshold function with the following parameters: method=’Pixel value’; Way=’Bottom’; Value=0.

 

Notes:

Fourier transformation is incompatible with masking, therefore masks have to be filled up with values. Set Protect MASK parameter to True in the 2D DFT Filter functions, when using masked images. This fills masks with zeros before transformation.

Images have to be quadrangular and size of power of two (e.g. 256, 512, 1024) pixels for fast filtering. Non quadrangular images may get distorted. To process non-quadrangular or non size of power of two images use the Enlarge paper feature of the 2D DFT Filters.

 

 

Reference List

 

   1.   Gerencser, A. A.; Adam-Vizi, V. Cell Calcium 2001, 30, 311-21.

   2.   Gerencser, A. A.; Nicholls, D. G. Biophys.J 2008, 95, 3079-99.