Temporal noise | EMVA 1288 — Machine Vision Test Standard | Color/Tone/eSFR ISO Noise |

The **European Machine Vision 1288 standard (EMVA 1288)** is designed to test several key qualities of linear image sensors, including linearity, sensitivity (quantum efficiency), noise, dark current, nonuniformities, and spectral sensitivity. * Imatest 2020.2* performs a subset of these measurements, including temporal noise and spatial nonuniformities in flat-field images. Results including Photo Response Nonuniformity and Dark Signal Nonuniformity (

*PRNU*or

*DSNU*for light and dark (“lens cap on”) images, respectively), can be calculated from batches of flat-field images in the Uniformity and Uniformity Interactive modules.

These measurements are derived from the EMVA 1288 standard and have similar numerical results, but they are not strictly EMVA 1288-compliant because the methodology is different. A sensor Dynamic Range measurement, is also designed to give results comparable to EMVA 1288, and again, it’s far from compliant.

Image sensor noise is a random variation of pixel levels caused by a number of factors— photons (shot noise), thermal (Johnson noise), dark current noise, and variations in the sensitivity and gain of pixels in the image sensor, sometimes called fixed pattern noise (which we will call spatial nonuniformity here. “Nonuniformity” is preferred in the EMVA standard (§4).

Image sensor noise can be decomposed into two fundamental factors.

**Temporal noise**, which is random noise that varies from image to image.**Spatial noise or nonuniformity**, caused by nonuniform pixel sensitivity and gain, which is consistent from image to image.

There are two ways of measuring temporal noise. Method 1 subtracts two images acquired under identical conditions, then divides by √2. Method 2 requires a large number of images. This method is used by the EMVA calculation because multiple images are also required to obtain spatial nonuniformity.

Calculating temporal noise and nonuniformity requires that multiple images be captured. (*L* ≥ 16 is the minimum recommended in EMVA §8; 100-400 is better, but the * Imatest* calculation will work with as few as 4 images (good for testing-only). The standard recommends capturing a set of light images whose mean pixel level (in linear files with no gamma applied) is 50% of saturation (designated by subscript 50 in the document; we prefer “light”) and also a set of dark pixels (“lens cap on”; designated by subscript dark).

μ = mean number of electrons per pixel ( _{e}μ = _{e}η μ). Imatest results are derived only from electrical measurements._{p }The notation in §8 is confusing, sometimes inconsistent, and often difficult to follow. For example, EMVA equation (42), \(\langle y\rangle = \frac{1}{L}\sum_{l=0}^{L-1}y[l]\) is not used after it is defined. The mean values Since there are many inconsistencies in the equations, and photometric units are often mixed with electrical or digital units, we are unable to follow the equations the standard exactly. The equations below represent actual μ represents the mean; s represents spatial standard deviations; σ represents temporal standard deviations. |

The mean of each individual pixel in \(\displaystyle\mu_s = \frac{1}{L}\sum_{l=0}^{L-1}y[l]\) Spatial nonuniformity The temporal noise variance (power) each individual pixel in the image is \(\displaystyle\sigma_s^2 = \frac{1}{L-1}\sum_{l=0}^{L-1}\left(y[l] – \frac{1}{L}\sum_{l=0}^{L-1}y[l]\right)^2 = \frac{1}{L-1}\sum_{l=0}^{L-1}\left(y[l] – \mu_s \right)^2 \) EMVA (44) This equation could be slow and tedious to evaluate, but there is a shortcut, described in the Wikipedia Variance page. In Wikipedia’s notation, \(E(x) = E[(x-E[x])^2] = E[x^2]-E[x]^2\). In the EMVA notation, \(\displaystyle\sigma_s^2 = \frac{1}{L}\sum_{l=0}^{L-1}y^2[l]\ – \left(\frac{1}{L}\sum_{l=0}^{L-1}y[l] \right)^2\) What this means in practice is that if you select The full EMVA 1288 Photo Response Nonuniformity ( \(\displaystyle PRNU_{1288} = \frac{\sqrt{\langle s_{y.light}\rangle ^2 – \langle s_{y.dark}\rangle ^2 } } { \langle \mu_{y.light}\rangle – \langle \mu_{y.dark}\rangle}\) where <…> denotes the mean taken over the image. Using only the light set of images, we can define PRNU_{1288}.\(\displaystyle PRNU_{light} = \langle s_{y.light}\rangle / \langle \mu_{y.light}\rangle\) Dark Signal Nonuniformity is \( DSNU = \langle s_{y.dark}\rangle\) Temporal noise (reported as a single number: mean for light or dark images) is \(\sigma_y = \langle \sigma_s\rangle\). |

**Method**

**Photograph** a flat field, which is typically a highly even light source, such as a non-flickering LED lightbox. For the bright images, if exposure control is available, choose an exposure to linear images are about 50% of the maximum level (this would be about 73% of maximum for a gamma = 2.2 color space).

**For saved image files**, open Uniformity or Uniformity Interactive, and select a group of *L* (light or dark) files. A confirmation window will open. Be sure to select **Read n files for pixel-based temporal noise (N >= 4). For EMVA-1288**.

**File confirmation window. Be sure to select Read n files … for EMVA-1288.**

A region selection window will open. Most of the time you’ll want to select the entire image (or use the same selection as the previous image, if you analyzed an image of the same size). Once you’ve made the selection, a progress bar will appear: reading multiple images goes surprisingly quickly.

**For direct data acquisition**, select the acquisition device with the Device Manager, which can be opened from the Settings dropdown menu in the Imatest main window, the Data tab in the box on the right, or the Uniformity Interactive Settings window. When you’ve made the selection, press **Save **.

**Device Manager. HD USB camera (1920×1080 pixels) has been selected. Press Save when ready.**

If possible, prior to acquiring the data, in the **Settings** dropdown menu, **Signal averaging** should be set to the desired number, and **Calculate image^2 while averaging** (which has the same function as **Read n files … for EMVA-1288**, above) should be checked. (This name may change.) It should be easy to repeat the data acquisition using the **Acquire image** (**Read Image File**) button on the bottom-left of the Uniformity Interactive window.

In the More settings window, **EMVA 1288** should be set to EMVA 1288 calculations: Box filter. The 5×5 Box filter is a highpass filter, described in §C.5, designed to suppress low-frequency spatial variations.

The **EMVA reset ** button on the right deletes EMVA 1288 batch results stored in imatest-v2.ini.

In the |

**Results**

Several plots, selected in the Display dropdown window, contain EMVA 1288 results. These include **Histograms**, **Accum. Histograms**, **V&H Spectrum**, **EMVA & Histogram**, and **Temporal noise image**.

**EMVA & Histogram** contains a summary of results.

**EMVA & Histogram results. (Some results are visible when the window is scrolled down.)**

When this plot is selected in Uniformity (the fixed module), the histogram (available in other plots) is omitted so the entire output can be seen.

**EMVA results from Uniformity (not Interactive)**

Some additional results are of interest.

**Standard histograms —** illustrated in EMVA §8.4, Figure 13. Can be calculated for light or dark images. Here are two examples, without and with the box filter, which is recommended by EMVA 1288 (§C.5) for removing low spatial frequency nonuniformities.

Histogram without Box (lowpass) filter |
Histogram with Box (lowpass) filter |

**Accumulated histograms —** illustrated in EMVA §8.4, Figure 14. We are not sure how to use them. Does not contain EMVA required results.

**Accumulated Histogram (with box filter)**

**Horizontal and vertical spectrograms and profiles —** described in EMVA §8.3 and 8.4. Combined here. These plots do not contain EMVA required results. Several smoothing settings are available.

**Temporal noise image —** Temporal noise power (variance) *σ*^{2} and RMS voltage *σ* as defined in the equations in the **green box** (above) are calculated for each pixel, i.e., they are *images*. For the flat-field images used in the EMVA calculations, temporal noise images are not of much interest, but they are of great interest for test chart images because they show how image processing varies across the image field. (When bilateral filtering is applied, noise is typically larger near edges than in smooth areas.) See **Temporal noise** for more details.