ProtocolsProtocols
Parameters of the Optical Flow algorithm
The parametering of the Optical Flow function strictly follows the equations and algorithms published by Gerencser & Nicholls1. The table below refers to the paper.
| Name | Default | Description |
| Select dx kernel: | [Savitzky-Golay first derivative] | Row kernel for differentiation in x. Kernel defined in Preferences or set parameters of the Savitzky-Golay kernel below. To be used in Eq.2. |
| Select dy kernel: | [Savitzky-Golay first derivative] | Column kernel for differentiation in y. Kernel defined in Preferences or set parameters of the Savitzky-Golay kernel below. To be used in Eq.2. |
| Select dt kernel: | [1,-1] | Column kernel for differentiation in t. Kernel defined in Preferences. Use the [1,-1] preset or set parameters of the Savitzky-Golay kernel below. To be used in Eq.2. |
| Average OF for dt width | Yes | Calculate OF using spatial derivatives of each frame, and then the average, to prevent biasing by leading and trailing edges. This is demonstrated by Fig.4. |
| Block mode | No | See block mode here. |
| SG kernel for dx,dy width | 3 | Width of spatial Savitzky-Golay 1st derivative kernel. Applied only if [Savitzky-Golay first derivative] is selected above. This was optimized in the paper (Fig.3). |
| SG kernel for dx,dy order | 2 | Order of spatial Savitzky-Golay 1st derivative kernel |
| SG kernel for smooth width | 7 | Width of smooth Savitzky-Golay 0th derivative kernel. Applied only if [Savitzky-Golay first derivative] is selected above. This was optimized in the paper (Fig.3). |
| SG kernel for smooth order | 2 | Order of smooth Savitzky-Golay 0th derivative kernel |
| SG kernel for dt width | 3 | Width of temporal Savitzky-Golay 1st derivative kernel. Applied only if [Savitzky-Golay first derivative] is selected above. The [1,-1] kernel was found to be ideal, so this parameter is not applied normally. |
| SG kernel for dt order | 2 | Order of temporal Savitzky-Golay 1st derivative kernel |
| Aperture kernel size | 5 | Aperture kernel is a matrix of ones. See Eq.3. |
| Aperture kernel shape | Box | Box or Disc. The paper used Box kernel. |
| Correct for bias by noise | Yes | Performs masking with Eq.6. |
| Correct low noisy gradients in time | Yes | Performs masking with Eq.5. |
| Enforce constraints on gradients in space | Yes | Performs masking with Eq.7 & 8. |
| Variance factor for time constraint | 1.5 | k-value defied in Eq.9. to be used in Eq.5. |
| Variance factor for bias | 1.5 | k-value defied in Eq.9. to be used in Eq.6. |
| Variance factor for constraint 1 | 4 | k-value defied in Eq.9. to be used in Eq.7. |
| Variance factor for constraint 2 | 0.45 | k-value defied in Eq.9. to be used in Eq.8. |
| Detector offset | equipment specific | Intensity measured in darkness, see "Sensor Noise Characteristics" |
| Detector variance vs. intensity Slope | equipment specific | Slope of noise diagram, see "Sensor Noise Characteristics" |
| Detector Read out Variance | equipment specific | Variance measured in darkness, see "Sensor Noise Characteristics" |
| Pixel size | 1 | Results are multiplied with this value (typically mm/pixel) . |
| Output as Absolute value of vectors | Yes | Pixel intensities in the output image mean absolute mm/s (or pixel/s if the above value is 1) |
| Output as X and Y components of vectors | No | Pixel intensities in the output image mean ±mm/s (or pixel/s if the above value is 1) |
| Output as Absolute value of Projected Vectors | No | Results Radial - anterograde/retrograde velocity image. Needs a projection point ROI below.' |
| Projection ROI | 1 | Center point ROI for radial projection. |
Changing/optimizing parameters of the Optical Flow algorithm
The above default parameters have been optimized for detection of motion of small (couple of pixels wide) objects/edges, the size that mitochondria typically show up in ~0.2-0.3 mm/pixel images. Parameters other than the equipment specific noise parameters, Pixel size and Block mode should be altered only with the understanding of the algorithm.
Setting up Optical Flow calculation for a given microscope / detector setting
The parameters below are calculated from the intensity-variance
diagram calculated from evenly illuminated fields. Calculation and
image acquisition with different image acquisition softwares are
given in the following protocol pages:
Elements,
Metamorph,
Zeiss LSM.
Noise
parameters:
The Pixel size is typically stored by the image acquisition software in the image file, and can be viewed by Image Analyst MKII by using the context menu Show Image Info of an Image Window, or the Tools/Setup DFT filter (this latter shows a default value if it was not recorded into the image file). Alternatively, for CCD cameras calculate the pixel size by dividing the physical pixel size by the lens magnification and by any other additional magnification (zoom or optovar, if present), and multiply by the binning.
The Block mode is always set to
No, when calculating Optical Flow in the Multi-Dimensional Open dialog (When using LSM files in block
mode, the Multi-Dimensionaldialog splits the blocks, so the Optical
Flow calculation is not performed in block mode). When a
complete time lapse is loaded first as non-processed, normal
Image Window, Optical Flow is calculated by the main menu
Special/
Optical
Flow function, and the Block mode is set
according to the organization of the
data.
Using more than 2 frames for Optical Flow calculation
Recording of two frames is sufficient to determine velocity vectors. If Optical Flow is calculated more than 3, e.g 5 or 7 (considering only odd numbers) of images, the temporal derivatives can be more accurately determined. However due to increased phototoxicity this is not advised. The dynamic range of the Optical Flow is calculated for the time span of the acquisition of all frames. Thus to keep the same dynamic range, when the number of frames is increased the acquisition interval has to be reciprocally decreased.
To calculate Optical Flow from larger number of frames set:
During continuous acquisition of Optical Flow this is a viable option to set the dynamic range of the Optical Flow calculation to lower velocities. In block mode or Multi-Dimensionalacquisition increasing number of frames leads to unecessarily phototoxicity. However recording more frames enables to adjust the dynamic range during data analysis.
The number of frames recorded in each short time lapse has to match the value of Select dt kernel (when using [1,-1] kernel, it is automatically 2). If more frames were recorded, the frames to be passed for Optical Flow can be selected in the Multi-Dimensional Open depending on the actual way of short time lapse generation:
Working with different resolution or gradient/object size
Using larger spatial differentiation and smooth kernels when working in large, dull objects or less sharp edges increases the dynamic range. However it will lead to inaccurate velocity determination over sharp edges. See Fig.3. of the paper1.
Tuning masking
The default variance factors were determined on modeled data, not on a specific microscopy system, therefore are assumed to be universal. Larger variance factors provide stronger masking (the Optical Flow algorithm is more conservative, and only edges most distinguishable from noise are passed)
References