The most misunderstood words in Earth Observation

Spatial resolution. We think we know what it means, but do we really? We wrote the following rant to clarify some confusion and make life easier for our future selves.

Written by Devis Peressutti and Matej Batič. Special thanks to Miha Kadunc, Maxim Lamare and Grega Milcinski for the invaluable feedback.

“What is the spatial resolution of this image?” must be high on the list of most frequently asked questions in Earth Observation (EO) and should definitely make it to the EO bingo card, along with “Can you count cars with it?” , “Can’t you just zoom-in more?” and “Is this a real-time video?”. In fact, spatial resolution is the bread and butter of any user of remotely sensed imagery, whether they know it or not, and is often a deciding factor for using one satellite imagery over another for a given application. However, we have noticed some inconsistencies and potentially misleading usages of the term “spatial resolution” which could cause confusion to someone new to the field, and sometimes to experts too.

In this post, we will focus on optical satellite imagery (radar imagery is way more complex) and try to shed some light over the most common answers to “What is the spatial resolution?”, which, in order of popularity, are probably pixel size, Ground Sample Distance and Ground Resolved Distance. These represent different quantities, and the fact that you might get three different answers to the same question should already cause you some head-scratching. If you have not yet heard for some of these terms, the post might be challenging to read, but worthwhile if you plan to work in the field.

Generally speaking, when we need to select an appropriate data source for a given application, e.g. land cover mapping, agricultural activity monitoring, building detection, we consider its spatial, spectral, and temporal resolutions. These resolutions typically define an overall image resolution that fully describes the optical imaging system. Resolution denotes the ability to distinguish elements that are separable in nature, i.e. features spatially separate, electromagnetic (EM) waves, and events temporally separable. The higher the resolution of the imagery, the more information it contains with the better power to resolve distinct quantities. Needless to say, the higher their cost as well.

These resolutions are typically defined for any optical digital imaging system, although for EO their meaning can differ slightly. In fact, in EO, temporal resolution refers to the temporal revisit window, rather than a frame-per-second relevant for high-speed cameras. Regarding spatial resolution in EO, we would expect an answer that reflects its general definition, namely, what is the minimum distance between objects that the system can resolve as separate? This is what we care about when building our beautiful applications. Why is it often so difficult to get this as an answer?

Why the pixel size is not equal to the resolution (in many many words)

Note: this section is quite a bit technical — if you get lost in variable names, feel free to skip to the next one. There might be bits and pieces lost, but you will still find the rest relevant.

To answer the last question, we have to refresh our memory on how optical satellite images are acquired. The sensor hardware design determines its signal-to-noise ratio, and its Instantaneous Field of View (IFOV), which is the solid angle through which a single detector (e.g. a cell element of the imaging sensor) is sensitive to radiation (Fig. 1). Once the satellite is in orbit, the flight height H and IFOV determine the Ground Resolved Cell, as GRC = H * IFOV (Fig. 3). The size of this cell determines the Ground Resolved Distance GRD. The energy reflected from features within the GRC is blended together into a single bin, preventing to resolve such features as separate. Therefore, the larger the GRC, the lower the spatial resolution.

Fig. 1. Schematic representation of the IFOV of two detectors, i.e. α and β, in an optical satellite imaging system. Given the same flight height H, the GRC of system β is larger than α, and therefore, the spatial resolution of β is lower than α. © 2022 Sinergise

Furthermore, the energy reflected by the target needs to be intense enough to be detected by the sensor [1], and, intuitively, the reflected energy signal increases if the signal is collected over a larger IFOV or if it is collected over a broader spectral bandwidth. This fact determines the trade-off between spatial and spectral resolutions, and is the reason why panchromatic sensors detect reflections over narrower IFOV and broader range of spectrum, while multi-spectral sensors typically have a wider IFOV but are sensitive to narrower EM spectra.

Single cell detectors are then typically packed in arrays, and Earth surface is imaged as the satellite moves forward (Fig. 2). This is referred to as the push-broom technology, which is used by a large number of optical satellites, e.g. NASA Landsat 8/9, ESA Sentinel-2, Airbus SPOT/Pleiades, Planet RapidEye, Maxar World-View. The number of detectors in the array, along with their IFOV and the flight height determine the swath width. The higher the satellite flies, the larger the swath width and the lower the spatial resolution. If you thought this is already too complicated, we have bad news. The above applies only to the GRD across-track, which is defined by the design of the detectors. The GRD along-track is determined by both the IFOV and the “shutter” that determines how long the sensor cells integrate incident light into the same row of pixels before switching to the next one.

Fig. 2. Schematic representation of push-broom technology, where the image is acquired in strips along the track of the satellite. The swath width is determined by the number of detectors in the sensor’s array, their IFOV and the flight height. Spatial resolution is defined separately across-track and along-track. © 2022 Sinergise

The combination of cell detector size and IFOV determines the Ground Sample Distance GSD, which is the distance between cell centres measured on the ground (Fig. 3). In an ideal case, the IFOV of neighbouring detector cells would not overlap, meaning that the GSD and GRD would be approximately equal. However, this depends on acquisition conditions and the quality of the detectors, e.g. cheaper detectors have larger IFOV. In addition, remember that most commercial satellites can acquire images off-nadir, resulting in longer distances from Earth than at nadir. That is why GSD is typically reported at nadir, and GSD/GRD off-nadir is larger, meaning, you guessed right, that spatial resolution off-nadir is lower. In general therefore, GRD is a more accurate proxy for spatial resolution than GSD. Both GRD and GSD are specific to the detectors, and therefore will be different for panchromatic or multi-spectral ones.

Fig. 3. Schematic representation of Ground Resolved Cell and Ground Sample Distance. In an ideal scenario, GRD would be equal to the GSD. However, the two distances can be different depending on the quality and design of the detectors. For sensors of lower quality and large IFOV, the overlap between neighbouring cells would be larger than the GSD. © 2022 Sinergise

So far so good (?). We can now move on to the raster pixel size, which is the quantity you are probably more familiar with. Pixel size is the size of each grid element of the raster image that you receive from the image provider. While the pixel size is correlated to the GSD, more often than not they are NOT equal, and usually pixel size ≤ GSD. This is because the raw radiometric signal is post-processed before it’s delivered to you, different post-processing leading to different product levels. Geometric post-processing includes reprojection and resampling to a fixed pixel grid, which is constant and independent of viewing angle and other variations in acquisition mode. In short, a pixel is still not a little square.

However, if the geometry of the detector, sizes of the single detector cells, the capabilities/resolution of the optical system, the instrument distance to Earth and instrument view angle are all optimised, then the GSD and GRD can be equal, and the image pixel size can also be equal to them. Being related to GSD and consequently GRD, pixel size could be used as a proxy for spatial resolution, however, more loosely so. In fact, if we took an image and simply resampled it to a smaller pixel size using linear interpolation, we would not have improved its spatial resolution. And this is where confusion can stem from, where pixel size is reported as the metric for spatial resolution, as is often done in super-resolution applications (more about this later on). Similarly, Sentinel Hub allows users to up-/down-sample the same data source at different pixel sizes, using different interpolation methods. Up-sampling your data source decreases the pixel size but does not change its GRD and spatial resolution. Conversely, down-sampling the data source increases its pixel size and diminishes its spatial resolution. Data providers can also provide down-sampled images for a lower price. This is the case for Maxar imagery available through Sentinel Hub, where World-View 3 imagery at original pixel size of 0.31 m is provided at a resampled 0.5 m pixels size (see Fig. 4).

What this all means in various EO missions?

At Sentinel Hub we are very lucky to have access to a variety of data sources, from low resolution to very high resolution (VHR) data. We analysed the GSD and pixel size of different commercial data sources over Dakar over several years, as part of the EDC Africa Urban Growth Contest. As you can see in Fig. 4, GSD values provided with the metadata of the images are larger than the pixel sizes reported in the products’ user guides. And yes, commercial providers typically report in their user guides pixel size as spatial resolution, although GSD at nadir and sometimes off-nadir is provided as well. You can easily repeat this analysis yourself since you can get all metadata as well as the images from Sentinel Hub

Fig. 4. Distribution of GSD values for different VHR commercial satellites over Dakar over several years. GSD is reported separately for the pan-chromatic and multi-spectral bands. Airbus Pleiades pan-sharpened images can have pixel size of 0.5 m or 0.7 m depending on the acquisition conditions and applied post-processing.

Fantastic. Let’s recap: we have seen that GRD is a better proxy for spatial resolution than GSD, which is a better proxy than pixel size, although pixel size is what is commonly reported (for simplicity?) in user manual guides and generally speaking. So we should just use GRD and be done with it. Well, in theory. The problem is that GRC or GRD are typically not reported in user guides, given their dependence on the detectors’ complex designs and acquisition conditions. So we need an alternative method to estimate GRD and, therefore, spatial resolution. We can do this by estimating the Modulation Transfer Function (MTF), or equivalently the Point Spread Function (PSF), of the optics, which define the low-pass filtering effect on the detected signal (Fig. 6). In an ideal scenario, the spatial frequencies that the system can detect without distortion are inversely proportional to the GSD [2], but since real things are not perfect as we have seen above, high spatial frequencies are distorted and filtered by the detector. Estimating the MTF/PSF allows to compare different sensors that have the same GSD, as shown below.

Fig 5. Comparison of two images with same GSD but different GRD and MTF. Image taken from the Airbus Pleiades user guide.

MTF is often not provided in user guides (with some notable exceptions, i.e. Sentinel-2 imagery), and in some cases the delivered images might already undergo deconvolution post-processing steps to try and revert this effect. What to do then? Well, we found an effort at standardising the image quality and performance of imaging systems through the National Image Interpretability Rating Scales (NIIRS), but we could find reference to this scale only in the Airbus Pleiades user guide, and not in any other image providers. In this case, the best we can do is look at the images and let them speak for themselves.

Fig 6. Visual representation of the low-pass filtering effect of an optical imaging system. The Point Spread Function, which describes the system’s response to an impulse, is the inverse Fourier transform of the Modulation Transfer Function, and characterises how the detected signal is distorted. The detected signal is given by the convolution of the original signal with the PSF. The larger the spread, the lower the spatial resolution, i.e. we cannot detect as separate the original objects. © 2022 Sinergise

Thankfully, there is a great deal of activity in calibration and validation of EO imagery, ensuring that the delivered products fulfill the specifications and that the satellite operates as expected. These activities are routinely performed to measure and validate the spectral and spatial resolutions, as well as the accuracy of the pixels’ geolocation. To evaluate the spatial resolution, man-made calibration targets, such as USAF 1951 Test Pattern, Bar Target, Slanted Edge and Siemens Star tests [2] are used to estimate the PSF and spatial resolution of the images. Examples of these calibration targets are shown in Fig. 7. A great collection of spatial calibration sites is provided by USGS.

Fig. 7. Example of spatial calibration sites with several calibration targets. FGI Sjökulla Aerial Test Range site in Finland (left), Baotou Comprehensive Calibration and Validation Site in China (middle) and NASA Stennis Space Center, USA (right). The calibration sites feature Slanted Edge tests, Siemens Star tests and Bar Target tests.

So, want to know the spatial resolution of your data source? Request the data source over a calibration site (e.g., Baotou) using the Third Party Data Import API and estimate the MTF and GRD from the Slanted Edge target and Siemens Star, according to the ISO 12233 standard. It mostly entails calculation of the edge profile, its derivative and Fourier transform, done over multiple line profiles to reduce aliasing and better estimate the MTF. ImageJ has plugins to automate this process as well. Too much work you say? Probably yes, so we can resort instead to the poor-man’s method: spatial resolution is the distance of the bar targets that I can see as separate by eye 👀, as shown in Figures 8 and 9. To get statistically relevant results, you would want to repeat the measurement under the same acquisition conditions multiple times, and average the estimates, so treat the results shown below with caution.

Fig 8. Airbus Pleiades and SPOT imagery over the Baotou calibration site in Spring 2021. The two top-most pictures show the PAN and red bands from the Pleiades satellite, while the two bottom-most pictures show the PAN and red bands from SPOT 6 satellite. Their GSD as reported in the metadata can be found below, along with their pixel size. Zoom-in of the target area shown below.

Table 1. GSD across and along track for the Pleiades and SPOT images shown in Fig. 8. As can be seen, GSD differs across and along the track of the satellite flight for acquisitions off-nadir. The pixel size is lower than the GSD and, as such, more loosely related to spatial resolution.

Fig. 9. Zoom-in of the calibration targets for the PAN and MS detectors of Pleiades (two leftmost pictures) and SPOT (two rightmost pictures). With these targets it is easier to appreciate the difference in spatial resolution of the detectors. The Siemens Star (target on the lower right of each picture) allows to estimate the spatial resolution by measuring the radius at which the aliasing effect is visible. MTF can be computed from the slanted edge target.

What to do with this new knowledge?

Now that we think we know a bit more about pixel size, GSD, GRD, MTF and PSF, the next question is, do we really need to know all these quantities? The answer is: it depends. You might want to know these when comparing different data sources for a given application. Say you want to create a building detection product, and want to choose the most suitable image source. Similarly, if you were puzzled because you couldn’t distinguish objects that are farther apart than the pixel size, you might want to check the GSD and estimate the MTF. Another application where we strongly feel GRD should be reported instead of pixel size is super-resolution, where the aim is to improve the spatial resolution of the input imagery by considering extra sources of information, such as temporal correlations or high-frequency features learnt from higher resolution imagery. Currently, the majority of super-resolution solutions report the pixel size of the super-resolved imagery, which tells very little about the actual improvement in spatial resolution, and makes comparison of different algorithms almost impossible. We have seen methods super-resolving Sentinel-2 to 3/2.5/1.25/1 m pixel size, but no information about the minimum distance between separate objects (possibly the real objects, not the hallucinated ones). The only exception we have found in this regard is from the research group behind TARSGAN [3] and OptiGAN [4], where estimates of MTF and GRD are reported and methods to estimate this over lines and edges is reported. We invite researchers in this topic to do the same (us included), to favour comparison of methods and avoid misunderstandings that hinder progress of the field.

Rant is over! Thanks for reading. Get in touch with us at eoresearch@sinergise.com for any question, comment, appreciation and complaint.

[1]: Pradham P., Younan N. H., King R. L. Concepts of image fusion in remote sensing applications. 2008, 393–428, doi.

[2]: Orych, A.: Review of methods for determining the spatial resolution of UAV sensors. Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., 2015, 391–395, doi.

[3] Tao, Y. et al.. Towards Streamlined Single-Image Super-Resolution: Demonstration with 10 m Sentinel-2 Colour and 10–60 m Multi-Spectral VNIR and SWIR Bands. Remote Sens. 2021, doi.

[4] Tao, Y. and Muller, J.-P. Super-Resolution Restoration of Spaceborne Ultra-High-Resolution Images Using the UCL OpTiGAN System. Remote Sens. 2021, doi.