## 2 Registration and Analysis of the Smartphone Recordings
### The Track Length Determination Algorithms  
There is, in general, high subjectivity to the interpretation of the images of long tracks with complex and complicated traces. Thankfully, these cases are rare, but they affect the tails of the track length distribution. The algorithm for the track length determination is especially sensitive to the treatment of the multi-component pictures, when the gaps in the traces are seen. After the projection of the pixel brightness along the identified track's main axis, the gaps in the histogram are clearly visible (see Figure 2) and the question then arises where the real particle track ends, if it is, of course, the real particle track in the first place. This question can be further expanded into more detailed ones: how long can the gaps be allowed in a single track, and how to treat the cases with the longer gaps. In principle, we can accept just the longer length regardless, or we can reject the entire frame from the track length distribution estimation procedure. We have tested several of these possibilities, noting as before that, with the appropriate method, the true cosmic ray muon tracks are expected to follow the power-law distribution of \(\cos(\Theta)\). The results of the six procedures are shown in Figure 3. The respective \(\cos(\Theta)\) distributions are shown there. To convert from \(l\) to \(\Theta\) (or to \(\cos(\Theta)\)), the depth of the camera's photosensitive layer is set here, for the time being, to 5 px. For simplicity we will, hereafter, measure all distances, and the track length, as well as the thickness of the matrix sensitive layer, using as a unit a single matrix pixel size (px). This is quite a natural unit if we are dealing with the same camera, as is in the case of the present work. The thickness of the photosensitive layer will be considered later in this paper. We explore in detail below the tested algorithms using the examples in Figure 3. Initially, we explore the steps within the least restrictive algorithm:  
1. acceptable gaps in the histogram tracks are of length up to 4 px (as shown in Figure 2) but exactly one track is seen in the picture,
2. as above up to 4 px gaps are accepted but'multiple track' events are included. In the middle row of Figure 3, we compared results of algorithms for'multiple track' cases (c) allowing events with large gap (up to 5 px) in the track,
3. only the small gap (only below 3 px) is acceptable. In the lower row of Figure 3, we present results for single-track cases and a very strong criterion for the gap length in the track
4. only 1 px long gaps, at most, are accepted,
5. no gaps at all are allowed. Most noticeably, we can see that the details of the algorithm used are primarily responsible for determining the very long tracks (large zenith angles) distribution. Rejections of the multiple tracks events affect mostly those very long tracks, which are about 1% of the overall population. Then the statistics of all plots in Figure 3 is very close to the total count of 60,000 regardless. We can now compare in detail the measured distributions obtained using the six algorithms described above, restricted to the 40\({}^{\circ}<\Theta<70^{\circ}\) region. The upper limit is based on a simple statistical argument and has practically no influence on the results of the fitting procedure. The lower limit of 40 degrees is related to the additional smoothing of the short track lengths due to the dimensions, and even the geometry, of the camera pixel matrix. An exact zenith track should give a track length of zero px, a slightly inclinedtrack may give a track length of 1 px (or even \(\sqrt{2}\)), if it passes through an edge. In addition, the actual structure of the camera matrix is obviously unknown (detailed pixel shapes, spacing, etc.). All of this makes the contents of the first few bins of the path length histogram difficult to interpret and thus difficult to correct for all these effects.