2.3.1. Methodology v1

In methodology v1, the test area was processed and divided into strips, and tests without and with overlay between the strips were performed. For the tests, the following assumptions were made.


For strips without overlay (methodology v1.1) and strips with overlay (methodology v1.2.), DTMmv1.1 and DTMmv1.2, respectively, were generated using the kriging method, and the results of processing all strips combined together were whole DTMv1.1 and whole DTMv1.2, respectively.

#### 2.3.2. Methodology v2

Methodology v2 differed from methodology v1 in that the DTMs were generated based on a reduced set. The reduction was performed by the OptD method. The tests were performed using similar assumptions to methodology v1.


DTMmv2.1 and DTMmv2.2 were obtained for methodologies v2.1 and v2.2, and DTMv2.1 and DTMv2.2 were obtained as a sum of partial DTMs, respectively. The scheme for the proposed methodologies is presented in Figure 2.

Additionally, for comparison, DTMs were generated from all the data (100%) and from all the data after reduction (2%):


Our approach used the OptD reduction method and the kriging interpolation method.

**Figure 2.** Scheme of the methodologies.

#### 2.3.3. OptD method

The main aim of OptD method was the reduction of the set of measurement observations. The degree of reduction was determined by setting prior, the reduction optimization criterion (*c*) (e.g., the number of observations in the dataset that the user required after reduction). Reduction itself was based on the cartographic generalization method. The area of interest was divided on measuring strips *L*. Within each *L*, the relative position of the points to each other was considered. The way how the points were tested in the context of being removed or preserved in the dataset depended on the tolerance range *t* related to the chosen cartographic generalization method. The width of *L* and *t* are iteratively changed until the optimization criterion was achieved. In result, there were different levels of reduction in the individual parts of the processing area: There were more points in the detailed part of the scanned object and much less within uncomplicated structures or areas. Only those points that were significant remained. This method has been described in detail in [35–37].

Previous applications of the OptD method consisted of processing the entire data set (airborne laser scanning—ALS, terrestrial laser scanning—TLS, mobile laser scanning—MLS). In the case of MBES, the strips with observations were reduced in almost real time and happened in stages. The OptD method was modified for this purpose. This modification relied on introducing in the OptD method a loop (FOR instruction) for fragmentary data processing. The methodology of processing MBES based on the modified OptD method is presented in Figure 3.

The strip's width can be determined or set in relation to the measuring speed. The first measurement strip is reduced while the next strip is acquired. The second strip is attached to the previous reduced strip, and then the second is reduced while the third is obtained and so on, until the measurement is finished. Reduction conducted within each of the separated strips is based on the Douglas–Peucker cartographic generalization method [45,46]. The process can be performed for strips without overlay (methodology v2.1) or strips with overlay (methodology v2.2). Finally, we obtained a whole data set consisting of reduced strips.


**Figure 3.** Processing of multibeam echosounders (MBES) data based on the Optimum Dataset OptD method.

In both versions, the optimization criterion, *c*, was adopted, which controls the reduction rate. For simplicity, this criterion was given as a percentage of points in the set after reduction. In this work, *c* = 2% was used, which is a high reduction rate. For almost real-time processing, processing time was important. Reduction decreased the number of observations, which substantially shortened the next process, DTM, and depth area generation. To generate DTM in almost real time, the kriging method was used.

In methodology v2.1, DTM1v2.1 was generated based on a reduced set with observations from the first measurement strip, p1. DTM2v2.1 was generated from p2 after the reduction, and the last interpolated node points were in the place where the DTM2v2.1 and DTM1v2.1 nodes coincided. The DTM3v2.1 nodes coincided with the nodes of the next DTM, DTM4v2.1, and the previous DTM, DTM2 v2.1, and so on. Methodology v2.2 used a similar process for strips with overlay.

Finally, the method gave the following models.


In addition to the DTMs generated by methodologies v2.1 and v2.2, DTMv2.1 and DTMv2.2 were obtained from the whole dataset after reduction. For comparison, using methodology v1, DTMmv1.1 and DTMmv1.2 and DTMv1.1 and DTMv1.2 were also generated.
