Table 1.
Area under the ROC curve for the five classification tasks of one species vs. the other four.
Table 2.
Area under the ROC curve for the ten classification tasks of one species vs. another one.
Figure 1.
Decision echo analysis for the classification task of spruce vs. the rest.
(A) Average spectrogram of the raw data of spruce. (B) Average spectrogram of the raw data of all the plants except spruce (i.e. the rest). The color bars for both (A) and (B) are in dB. (C) The difference of the preprocessed spectrograms of spruce and the rest. (D) The normal vector (decision echo) to the separating hyperplane calculated for this classification task. In both (C) and (D) black represents negative values, white represents positive ones, and gray is zero.
Figure 2.
Decision echo analysis for the classification task: corn vs. the rest.
(A) Average spectrogram of the raw data of corn. The color bars for both (A) and (B) are in dB. (B) Average spectrogram of the raw data of all the plants except corn (i.e. the rest). (C) The difference of the preprocessed spectrograms of spruce and the rest. (D) The normal vector (decision echo) to the separating hyperplane calculated for this classification task. In both (C) and (D) black represents negative values, white represents positive ones, and gray is zero.
Figure 3.
The results of generating hybrid sepctrograms of apple and corn.
Only (B) and (D) were artificially generated. Color bars are not presented, but the data are in the spectral power scale. (A) Average spectrogram of apple. (B) The decision echo multiplied by η = 0.07 added to the average spectrogram. (C) The average spectrogram of corn and apple. (D) Same as B, but with η = −0.07. (E) Average spectrogram of corn. (F) The decision echo calculated for this task used to create (B) and (D). Dark intensities depict negative values, while white depict positive ones. (G) Classification performance of echoes created from artificial hybridized spectrograms as a function of the η factor. To measure performance we divided the spectrograms of each species into 10 groups, each containing 50 spectrograms with a similar η. The units of η are relative, such that η = 1 corresponds to an artificial spectrogram that is as distant to the hyperplane as the most distant original spectrogram. The performance is measured in the percentages of echoes that were correctly classified according to the expected classification.
Figure 4.
Spectrograms of the weighted support vectors on each side of the hyperplane.
The color bars are in dB. (A) The apple spectrograms used as support vectors added up according to their weights. (B) Same as A for corn. Examining the two weighted spectrograms, the idea of the support vectors, being the most difficult data points to separate in the limits of the data set, becomes clearer.
Figure 5.
Classification performance of four classification tasks when using partial data of the spectrograms for classification.
Each pixel represents the performance when using a square from the spectrogram with a frequency band of 5 kHz and time duration of 5 ms. The color denotes the area under the ROC curve (AUC) when classifying using only this square of information from the spectrograms. The classification tasks presented are: (A) Spruce vs. the rest; (B) Blackthorn vs. the rest; (C) Beech vs. the rest; (D) Corn field vs. the rest.
Figure 6.
Effect of the DFT window length on classification performance.
(A) The area under the ROC curve (AUC) for four different window lengths ranging from 250–2000 µs. Average results are presented together with the blackthorn classification case, in which the effect was most clear. The difference between a 2000 µs window length and the other lengths is significant (P<0.05), whereas the difference between the three other lengths is not. (B) Average spectrograms for a window length of 2000 µs (first row) and a 250 µs one (second row) for the classification task of blackthorn vs. the rest. It can be seen how time information is decreased (i.e. smeared) for the 2000 µs window (first row). This makes separation between the two classes easier with the 250 µs window (second row) even when only examining them visually.
Figure 7.
The area under the ROC curve (AUC) for all of the broad-leaved trees pair-wise classification, when using partial information from the spectrograms, limited to frequency bands of 10 kHz.
The graphs show a relative preference for the low frequencies information, but the exact slope is task-specific.
Figure 8.
The correlation between the distance from the separating hyperplane and the fourth moment of the echoes.
o – regular data point, * – support vectors. Correlation values are indicated in rectangles in upper right corner. (A) The comparison for the task of classifying apple and spruce reveals a high correlation between the distance and the fourth moment. (B) The comparison for the task of classifying beech and blackthorn reveals no correlation between the distance and the fourth moment, implying that the fourth moment cannot be used to classify the two. This figure also visualizes how the task in (A) is easy for the SVM compared to the one (B).
Figure 9.
Summary of the materials and methods.
(A) The basic setup of the experiments, in which a sonar head on a tripod was used to ensonify plants. The emitted signal's spectrogram is presented with the time signal under it and the frequency dependent intensity curve on the right. (B) An example of a time domain back scatter recorded from a single apple tree. The amplitude is in arbitrary units. (C) The spectrogram of the time domain signal of B, created after cutting the echo out of the time signal. The spectrogram's frequency range was cut between 120–25 kHz, and it was threshold leaving only the regions that are high above noise. (D) An illustration of the classification by SVMs. Following PCA, each spectrogram is represented by a 250-dimentional data point (shown in the figure as a 2-dimentinal point) belonging to one of two classes (circles or rectangles). The SVM then learns the best hyperplane for the training data. The data points that are closest to the hyperplane (denoted as full shapes) are called the support vectors and define the orientation of the hyperplane.
Figure 10.
In all rows the species from left to right are: apple, spruce, blackthorn, beech, and corn field. In all spectrograms, color bars are in dB. The units in the time signals are arbitrary. (A) The average spectrogram of each plant species. (B) The average envelope of the time signal of each plant species. (C) The corresponding example of a single spectrogram of each plant species (the effect of applying the threshold is noticeable). (D) The corresponding example of a single echo of each tree in the time domain.