How a global camera sensor map helps you to find differences between cameras using supervised multivariate classification method.

In almost all of the reviews on the internet that I have seen so far there is the so called one to one comparison tradition between camera sensors;  for example they look at different sensor characteristics beside each other and score which one is better or worse. The danger of using this univariate approach and related techniques are that such tests do not consider how (sensor) variables combine together to form a diagnostic pattern. They are often misleading and inefficient. So I am going to address this here again with a more advanced multivariate approach.

As explained in the previous posts, Principal component analysis (PCA) is an unsupervised approach that is usually the first and rather quick data screening step where it helps to maximize variability between different samples. This would help to pick up the trends ,differences, structure or anomalies in the data. So for the next step we can use a supervised classification method like Orthogonal Projections to Latent Structures (OPLS). The advantage with this technique over PCA (unsupervised) is that it separates orthogonal data (irrelevant/noise to the model) to maximize the covariance in the data which enables to explain the presence of a latent and systematic structure in a model. It can greatly help finding out why a data-set is structured in a certain manner.  OPLS can give you the chance to view the data structure (if any) at different angles and to identify class differences; so you may want to ask yourself what would you want to inspect in your data.

There are lots of sources on the internet that you can read about OPLS but for the sake of this article I have done the OPLS modeling on the same data-set that I used for PCA modeling.  Explaining everything into fine details takes quite bit of a time but I keep this brief. When the name “variable(s)” comes in the text in this article, that would indicate read noise, Quantum Efficiency (QE), Photographic Dynamic Range (PDR), Low Light ISO in EV (LLEV), pitch, Full Well Capacity (FWC) and sensor size.

So what the model do on the data is to classify different sensor data points in a way that they look like wrapped into virtual envelopes (in this case five envelopes!). Figure 1 shows how beautifully sensor form factors have been classified based on the sensor variables. The influence of each variable on the sensor classification is shown in figure 2. The X and Y axis show variations between and within sensor classes.

 

OPLS_QE as Y

Figure 1 – OPLS model of the camera sensor data – R2(cum)= 0.827 Q2(cum)= 0.513, P (model significance) = 3.68e-16      Download larger image.

 

sensors and loadings

Figure 2 –  Each variable (arrows) pulls data towards its direction like an invisible string and hence cause the separation between sensors. The strength of each variable depends on the amount of loading it has on the model. Download larger image.

Visually verifying the similarity (proximity to each other) of these data points with Dpreview’s side by side RAW and dynamic range image analysis will produce very similar results as expected. Looking at ISO values at 3200 or higher and EV at higher shadow stops would make the comparison easier, for instance by checking the sensor data points that are clustered close together, for:

Full Frame class

(D610, D750 and DSC-RX1) | (EOS 1DX Mark II, EOS 5D Mark IV, D800E, ILCE-9 and ILCE-7R)|(D4, Df, ILCE-7 and SLT-A99V) | (Z7, D850 and ILCE-7RM3) etc.,

Cropped sensor class

(D500, D7500, D7200, ILCE-6300 and ILCE-6500) | (EOS 200D, EOS 80D and D3300) etc.,

MF3 class

(OM-D E-M10, OM-D E-M10 Mark II, OM-D E-M5 Mark II and Lumix DMC-GH4) etc., in this sense I believe OM-D E-M1 Mark II is a different animal!

In this context to be honest some camera sensor scoring approach on the Net makes me scratching my head!

Also with this approach, valuable time to go through pages of reviews, speculations and side by side benchmarks can be saved. Needless to mention what course has been taken to improve sensor quality throughout these years, take a wild guess or check figure 3!

Time_Trend

Figure 3 – Manufacture year of the sensors in correlation with sensor variables. It is clear that sensor manufacturers have been trying to decrease read noise and increase QE, PDR and LLEV at the same time or at least to find a balance between them. These are the same data points as in figures 1 and 2. Download larger image.

Acknowledgement: I would like to thank Bill Claff (photonstophotos.net) for his permission to use his data for this work.



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