# Metric analysis for spatial semantic segmentation of sound scenes

Mayank Mishra, Paul Magron, Romain Serizel

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Mayank Mishra, Paul Magron, Romain Serizel. Metric analysis for spatial semantic segmentation of sound scenes. 2026. hal-05443978

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METRIC ANALYSIS FOR SPATIAL SEMANTIC SEGMENTATION OF SOUND SCENES

Mayank Mishra, Paul Magron and Romain Serizel

Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France

ABSTRACT

Spatial semantic segmentation of sound scenes (S5) consists of jointly performing audio source separation and sound event classification from a multichannel audio mixture. To evaluate S5 systems, one can consider two individual metrics, i.e., one for source separation and another for sound event classification, but this approach makes it challenging to compare S5 systems. Thus, a joint class-aware signal-to-distortion ratio (CA-SDR) metric was proposed to evaluate S5 systems. In this work, we first compare the CA-SDR with the classical SDR on scenarios with only classification errors. We then analyze the cases where the metric might not allow proper comparison of the systems. To address this problem, we propose a modified version of the CA-SDR which first focuses on class-agnostic SDR and then accounts for the wrongly labeled sources. We also analyze the performance of the two metrics under cross-contamination between separated audio sources. Finally, we propose a first set of penalties in an attempt to make the metric more reflective of the labeling and separation errors.

**Index Terms**— semantic segmentation, audio source separation, sound event classification, evaluation metrics

1. INTRODUCTION

The use of machine learning is becoming ubiquitous in today's daily life, since it has helped in tackling more complex problems than ever and opened opportunities for application in technology aimed at specific needs. In particular, machine listening, which aims at designing systems that automatically analyze audio scenes [1], has found novel applications to home assisted living and immersive communication in smart homes and smart cities [2-4].

Spatial semantic segmentation of sound scenes (S5) is a recent task, which aims at performing audio source separation and audio classification from a multi-channel audio input [5, 6]. S5 is a step towards the development of audio systems that could help in analyzing audio scenes, and it is of particular importance in technologies to be used in home assisting living and immersive communications. Since S5 is a combination of two sub-tasks, one way to evaluate S5 systems is to evaluate audio source separation and classification separately by using respective metrics for each sub-task [7, 8]. Another possibility is to consider one of the two tasks as a primary task and evaluate the systems based on the metrics for that primary task. This is what was done to evaluate sound event detection and separation, a problem close to S5 but where sound event detection was considered as a primary task over source separation [9]. However, for certain applications both tasks are equally important. For example in immersive communications the audio streams need to be properly separated before transmission and they need to be properly classified in order to select the correct streams to transmit. The metric then needs to reflect both the separation and classification performance.

To that end, a class-aware signal-to-distortion ratio (CA-SDR) metric was proposed and used in the DCASE 2025 challenge [5].

CA-SDR utilizes a combination of an audio separation metric, the signal-to-distortion ratio (SDR) [7, 10, 11] weighted by the true positives (TP), false positives (FP) and false negatives (FN) obtained based on the class allocations done by the system. This approach puts a strong emphasis on classification by using the class labels allocated by the system regardless of the similarity between the separated sources. This approach can tend to overlook potential permutation between sources.

We propose a new metric for the evaluation of S5 system called class and source aware SDR (CASA-SDR). The metric takes into account the similarity between the predicted and reference sources before computing classification performance. The goal of CASA-SDR is to provide an alternative that alleviates certain shortcomings of CA-SDR. We identify possible separation and classification error scenarios for S5 and compare the behavior of the metrics on these error scenarios. We identify possible pitfalls of each metric, and propose further improvements to alleviate these. We introduce penalties on CASA-SDR to better reflect the classification errors made by an S5 system, making it more informative.

2. PROBLEM STATEMENT

2.1. S5 definition and setup

The S5 task assumes the following setup [5, 6]. We consider *M* sound sources (*u*₁, ..., *u*ₘ) that are distributed in a room. Among those sources, the first *N* sources (*N* < *M*) are considered as target sources, and the remaining *N* - *M* sources are considered as non-target sources (interferences). Each source is associated with one sound event that is active at some point within the duration of the signal, and whose label is denoted *c*ᵢ, such that *C* = (*c*₁, ..., *c*ₙ) denote the set of true target class labels.

For the non-target sources the class of the sound events are considered unknown.

The goal of an S5 system is to estimate each of the target sources that are present in the mixture, as well as their respective class labels. For the remainder of the paper, in order to simplify the analysis and to match closely the task setup proposed in Nguyen et al. [5], we consider that the mixture consists of a total of *M* = 5 active sources with *N* = 3 target and 2 interfering sources. Note however, that the metric proposed here applies to more general scenarios.

2.2. Classical SDR

In its most basic form, the SDR between a true and estimated signal, respectively denoted *s* and *ŝ*, is defined as:

$$
\text{SDR}(\hat{s}, s) = 10 \log_{10} \left( \frac{\| s \|^2}{\| \hat{s} - s \|^2} \right). \qquad (1)
$$
In the context of source separation, it is customary to compute a permutation-invariant variant of the SDR [7] as follows:

$$ \frac{1}{N} \sum_{i=1}^{N} \text{SDR}(\hat{u}_i, u_i), \qquad (2) $$

where $(\hat{u}_1, \dots, \hat{u}_N)$ is the set of estimated sources, and $\hat{u}_i$ is the permuted estimated source with the highest similarity with $u_i$, i.e., such that this set of permuted sources yields the highest possible total SDR according to Eq. (2). We refer to it as the classical SDR.

## 2.3. CA-SDR

The classical SDR defined above is straightforward to compute, but it does not take the class labels into account, thus the CA-SDR was proposed to also evaluate sound event classification [5, 6]. Let $\hat{C} = (\hat{c}_1, \dots, \hat{c}_N)$ denote the predicted class labels associated with $(\hat{u}_1, \dots, \hat{u}_N)$. Then, the CA-SDR is defined as follows:

$$ \text{CA-SDR} = \frac{1}{|\mathcal{K}|} \sum_{k \in \mathcal{K}} \text{SDR}(\hat{u}_k, u_k), \qquad (3) $$

where $\mathcal{K}$ is the set of source indices such that $c_k \in C \cap \hat{C}$. Using the above definition, the CA-SDR evaluates the S5 systems on both the separation and classification tasks as follows:

* Identifying the sources corresponding to the TP, FP, and FN by comparing the set of predicted labels and the set of reference labels.

* Computing the SDR only for the sources that were correctly classified (TP), and sets the SDR at zero for the sources that were not classified correctly (FN, FP).

* Taking the mean of the metric over all three sources.

Note that as proposed by Nguyen et al., a penalty could be set for the sources that were not classified correctly [5]. In this paper, we follow the setup used in Yasuda et al. [6] and the penalties are not used for CA-SDR.

## 2.4. Limitations of CA-SDR

Here we present possible limitations of CA-SDR. This metric is computed on an ordered set of estimated sources that is obtained based on the class allocated to each source by the S5 system. This approach considers the set of classes that are predicted over all the estimated sources to compute classification errors, and assigns an estimated source to a matching target source of the same class. This potentially overlooks cases where source are correctly separated but allocated an incorrect class, or not allocated any label.

A first case described in Table 1 consists of two sources being allocated classes that are present in the original mixture ("cough" and "pour"), while the third source is not allocated any class. The CA-SDR matching will associate target sources and estimated sources based on their classes so their will be two TP for "cough" and "pour" and the third source is considered a FN as if "dishes" was not detected. The SDRs are computed for the sources assigned "cough" and "pour". We get an expected SDR value unless the source that was allocated the label "pour" was actually containing "dishes" (as in Table 1). This can be detected by matching the sources based on the optimal SDR obtained on all the possible sources permutations (as described above). The source that was assigned the label "pour" is then denoted $\hat{u}_2$ as it best matches with the target source $u_2$. When using CA-SDR matching this source mis-allocation will

<table><caption>**Table 1.** CA-SDR and optimal SDR based sources matching when one estimated source is not allocated the proper label ($\hat{u}_2$, cough) and one estimated source is not allocated any label ($\hat{u}_3$, none). The boldface font indicates which of the terms (separated source or predicted classes) is used for the source matching.</caption><thead><tr><th rowspan="2">References</th><th colspan="4">Predictions matching</th></tr><tr><th colspan="2">CA-SDR</th><th colspan="2">Optimal SDR</th></tr></thead><tbody><tr><td>(u<sub>1</sub>, cough)</td><td>(*û<sub>1</sub>, cough)</td><td>TP</td><td>(*û<sub>3</sub>, cough)</td><td>TP</td></tr><tr><td>(u<sub>2</sub>, dishes)</td><td>(*û<sub>3</sub>, none)</td><td>FN</td><td>(*û<sub>2</sub>, pour)</td><td>FN+FP</td></tr><tr><td>(u<sub>3</sub>, pour)</td><td>(*û<sub>2</sub>, pour)</td><td>TP</td><td>(*û<sub>3</sub>, none)</td><td>FN</td></tr></tbody></table>

<table><caption>**Table 2.** CA-SDR and optimal SDR based sources matching when one estimated source is not allocated the proper label ($\hat{u}_1$, dishes) and ($\hat{u}_2$, cough).</caption><thead><tr><th rowspan="2">References</th><th colspan="4">Predictions matching</th></tr><tr><th colspan="2">CA-SDR</th><th colspan="2">Optimal SDR</th></tr></thead><tbody><tr><td>(u<sub>1</sub>, cough)</td><td>(*û<sub>2</sub>, cough)</td><td>TP</td><td>(*û<sub>1</sub>, dishes)</td><td>FN+FP</td></tr><tr><td>(u<sub>2</sub>, dishes)</td><td>(*û<sub>1</sub>, dishes)</td><td>TP</td><td>(*û<sub>2</sub>, cough)</td><td>FN+FP</td></tr><tr><td>(u<sub>3</sub>, pour)</td><td>(*û<sub>2</sub>, pour)</td><td>TP</td><td>(*û<sub>3</sub>, pour)</td><td>TP</td></tr></tbody></table>

reflect on a low SDR value (SDR($\hat{u}_2, u_3$)) which could be interpreted as either bad separation or classification error. When matching the sources based on the optimal permutation in terms of SDR this mis-classification becomes explicit (cf. the rightmost column).

A similar behavior is observed in a second case described in Table 2, where all sources are allocated one of the label that was present in the original mixture, but two sources' labels are swapped ("dishes" and "pour"). Here there are now two FN+FP and a TP while the CA-SDR calculates the results as if there are three TP. The SDR relative to the sources classified as "cough" (SDR($\hat{u}_2, u_1$)) and as "dishes" (SDR($\hat{u}_1, u_2$)) will be very low (possibly negative) as the estimated sources are not match to the correct target sources. This could be the sign of a poor separation or an incorrect classification. When matching the sources based on the optimal permutation in terms of SDR this source swapping becomes explicit (cf. the rightmost column).

In both cases, classification error can reflect in SDR as low SDR values (as long as the classes predicted are in the set of classes present in the input mixture). This is ambiguous as low SDR could also reflect properly classified sources but with poor separation.

# 3. PROPOSED METRIC

In this section, we present CASA-SDR,<fnref n="1" /> and we discuss how it alleviate the limitations of the CA-SDR discussed above.

## 3.1. CASA-SDR

CASA-SDR uses the following procedure for S5 evaluation:

* Instead of first calculating the labeling errors on the predicted labels, we first calculate the SDR between all possible pairs of reference and estimated sources, i.e., we compute the SDR over all possible source permutations.

* We select the best source permutation, i.e., the permutation of estimated sources that provide the matching target sources/estimated sources with the highest SDR value. We also apply the same permutation to the class labels so that

<footnote n="1">¹The code will be released upon publication.</footnote>
(sources, label) tuples remain as predicted by the S5 system before the permutation phase.

* We calculate the classification errors given the permutation of the sources obtained above.

* We only keep the score for sources with correct labels (TP) and we assign a 0 dB score to sources with incorrect labels.

* We compute the mean over all target sources.

The above modification allows for controlling the impact of the FP/FN on the metric, while in CA-SDR these errors can reflect in either a 0 dB or low SDR. In essence, when there are labeling errors, e.g., as described in Tables 1, 2, CASA-SDR avoids assigning a low (sometimes negative) SDR that could be ambiguous as it always takes the best permutation of sources for SDR calculation. Hence with CASA-SDR, a low SDR means a poor separation and the classification errors are marked explicitly.

## 3.2. Penalties for mis-classification

CASA-SDR helps identifying if the system made a classification error by explicitly making the difference between poor separation of properly classified sources and misclassified sources. However, using the definition above, the CASA-SDR set the SDR at 0 dB when there is a classification error. In an attempt to emphasize the classification errors in the metric, we introduce the following penalties on SDR values. These are designed to be consistent in term of computation with the SDR for correctly labeled sources as they are ultimately going to be aggregated together. Penalties take positive values only, and they are subtracted to the overall CASA-SDR during the averaging phase.

**Input level penalty (IP)** This penalty value is equal to the SDR between the mixture $x$ and each considered target source $u_i$, with a 0 dB threshold to avoid negative values. Hence in case of a misclassified source, instead of setting the corresponding score at 0 dB, we replace it with $-\max(\text{SDR}(x, u_i), 0)$ before averaging across sources. The motivation is that if a source is salient in the input mixture, then making errors on that source should be heavily penalized.

**Output level penalty (OP)** This penalty value is equal to the SDR value of the wrongly labeled source, which is obtained with the optimal source permutation, see Section 3.1. Therefore, in case of a misclassified source, instead of 0 dB we set the score at $-\text{SDR}(u_i, *\hat{u}_i)$ before averaging across sources. The motivation is that if a source was properly estimated (high SDR) then classification errors on that source should be heavily penalized.

## 3.3. Application of penalties

We consider two possible ways to apply these penalties, leading to two different versions of the CASA-SDR.

**Non-TP based** The penalty is applied once when a source is not labeled correctly. One problem with this approach is that FP, FN and swapping (FP+FN) are penalized equally. By default, CASA-SDR follows this approach.

**Error based (EB)** The penalty is applied once for each classification error. This leads to different penalty values for FP, FN and swapping (FN+FP). This approach can be considered as over-penalizing swapping, since it introduces four penalties for each swapping between two sources (2 penalties for each swapped source).

<table><caption>**Table 3.** Classification error types on a two sources example.</caption><thead><tr><th>References</th><th>Type 1 (deletion)</th><th>Type 2 (substitution)</th><th>Type 3 (swapping)</th></tr></thead><tbody><tr><td>(u<sub>1</sub>, cough)</td><td>cough</td><td>cough</td><td>dishes</td></tr><tr><td>(u<sub>2</sub>, dishes)</td><td>none</td><td>telephone</td><td>cough</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Comparison of metrics in case of cross-contamination.</figcaption></figure>

# 4. EXPERIMENTAL PROTOCOL

## 4.1. Dataset

In order to evaluate CA-SDR and CASA-SDR, we design a custom dataset based on the dataset proposed by Yasuda et al. [6]. To do this, we used the Spatial Scaper library [12] to generate audio mixtures using a subset of the FSD 50k dataset [13]. We generated 10 second-long audio mixtures using room impulse responses (RIRs) available in the Spatial Scaper toolbox. We cropped the RIRs at 50 ms in order to discard the late reverberations, such that the setup is close to that proposed by Yasuda et al. [6], who conducted evaluation on dry sources. We then combine these audio sources from distinct target classes to generate audio mixtures. We generated 500 audio mixtures with a total of 5 sources out of which there were 3 target sources.

## 4.2. Impact of classification errors

First, we focus on the impact of classification errors on the metrics' behavior. We analyze the metrics on S5 with an oracle source separation setup (i.e., without cross-contamination between the separated sources). We introduce labeling errors of three types on the predicted sources: deletion, substitution and swapping (Table 3). We calculate the classical SDR, CA-SDR, and CASA-SDR after addition of white noise at 10 dB signal-to-noise ratio (SNR).

## 4.3. Impact of source cross-contamination

In order to focus on the impact of cross-contamination between the sources, we fix the predicted labels as correct (oracle classification). We progressively cross-contaminate the predicted sources by adjusting a scaling factor $\alpha \in [0, 1]$ to control the amount of interference.

We considered different cases of cross-contamination, but for clarity here we focus on the following most-informative case where two sources are gradually swapped as $\alpha$ increases from 0 to 1 and the third source is kept the same as the reference.

$$ \hat{u}_1 = (1 - \alpha) \cdot u_1 + \alpha \cdot u_2 + \epsilon, \quad (4) $$

where $\epsilon$ is a 60 dB additive white noise to avoid infinite values during calculations, and similarly for $\hat{u}_2$.
<figure><img src="image_4.png" /><figcaption>Fig. 2. CASA-SDR under various penalties for type 3 errors.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. EB penalty application for various error types.</figcaption></figure>

## 4.4. Penalty analysis

Finally, we analyze the impact of adding penalties onto CASA-SDR. We follow a similar setup as described in Section 4.2 except that the penalties are added according to non-TP based and EB strategies. To simulate practical scenarios, we add white noise at either 6 dB SNR, which is close to the CA-SDR value for the baseline model of Nguyen et al. [5], or 30 dB SNR, which corresponds to an almost-clean source estimate.

# 5. RESULTS AND DISCUSSION

## 5.1. Impact of classification errors

In Table 4, we present a comparison between the classical SDR, CA-SDR, and CASA-SDR for different types of classification errors. We observe that for type 1 and 2 errors, both CA- and CASA-SDR produce similar values since in these cases there are two TPs, and the metrics assign a 0 dB value to the other source. Type 3 error results in different SDR values for the three metrics. This is due to the source matching process that is different in CA- and CASA-SDR. For CASA-SDR, with the SDR of two sources set to 0 dB and the third one to 10 dB, we obtain a metric value of 3.33 dB. CA-SDR on the other hand calculates SDR on one correctly aligned source (positive SDR) and two swapped sources (negative SDR), which results in an overall negative value.

This experiment shows that the classical SDR is not well-suited for the S5 task as it returns the same value irrespective of the classification error. On the other hand, CA-SDR heavily penalizes the errors of type 3 in comparison to the other two types. While CASA-SDR does not differentiate between errors of types 1 and 2, it does help in identifying type 3 errors. Therefore, in this regard it is more insightful than the classical and CA-SDR variants.

<table><caption>Table 4. Metric values (in dB) at 10 dB SNR.</caption><thead><tr><td>Metric</td><td>Type 1 (deletion)</td><td>Type 2 (substitution)</td><td>Type 3 (swapping)</td></tr></thead><tbody><tr><td>Classical SDR</td><td>10.00</td><td>10.00</td><td>10.00</td></tr><tr><td>CA-SDR</td><td>6.67</td><td>6.67</td><td>-0.68</td></tr><tr><td>CASA-SDR</td><td>6.67</td><td>6.67</td><td>3.33</td></tr></tbody></table>

## 5.2. Impact of source cross-contamination

We now analyze how the metrics behave under cross-contamination between the sources, such that two of them are gradually swapped as described Section 4.3). The results are displayed in Figure 1. While all metrics decrease similarly as $\alpha$ increases, they behave differently for $\alpha > 0.5$. The classical SDR increases with $\alpha$, CAS-SDR continues decreasing while the CASA-SDR becomes constant. When $\alpha > 0.5$, classical SDR increases because the permutation matches the swapped sources with the correct target source. CAS-SDR is decreasing as the SDR between the swapped source and the target source is decreasing but because of the source matching process CASA-SDR does not detect any classification error. In CASA-SDR on the other hand, the swapped sources are correctly matched thanks to the permutation but the metric detects the classification errors and sets the SDR of the corresponding sources to 0 dB. Hence, we can see again that CASA-SDR is better suited than CAS-SDR for identifying label swapping occurring due to poor source separation.

## 5.3. Penalty analysis

In Figure 2, we present the impact of IP and OP penalties on CASA-SDR for type 3 errors. For the IP we see that it is slightly lower than the CASA-SDR without penalty. This difference remains stable for both SNR values. An explanation is that the added diffused noise has little impact on the source to mixture SDR. For OP, we can see that the penalties have a much larger effect and can drive CASA-SDR to negative values. This difference is even more pronounced at 30 dB SNR when the sources are well separated and the output SDR is high. The SDR difference observed at 6 dB and 30 dB SNR highlights the fact that the penalties are applied in proportion to the separation quality. One limit here is that OP can become unreasonably large when sources are well separated.

In Figure 3, we focus on the application of penalties and present the impact of the different strategies to add penalties depending on error types. We can see that for type 1 and 2 errors, CAS-SDR, CASA-SDR without penalty, and CASA-SDR with OP are similar, so these metrics do not allow for making the difference between these error types. The OP (EB) behave differently on type 1 and 2 errors. This is consistent with how the penalties are applied in OP and OP (EB). For type 1 error, since there is only one FN, both metrics are penalized only once, leading to similar results. However, for error type 2, we have an FP and an FN, which are penalized only once in OP and twice in OP (EB), resulting in lower (here 0 dB) value of the metric when averaging. With type 3 errors, all metrics are different but the OP (EB) is heavily penalized because of the 2 FP and 2 FN induced by source swapping.

# 6. CONCLUSION

In this paper we analyzed the CAS-SDR metric for evaluating S5. We highlighted potential limitations of this metric. We proposed an alternative CASA-SDR metric, which refines identifying separation
and classification errors. We also introduced a set of penalties for CASA-SDR that allow to better capture the type of errors done by an S5 system. We analyzed the behavior of multiple version of CASA-SDR based on these penalties, and compared them to the behavior of CA-SDR. The proposed framework allows for tuning the metric based on the targeted application scenario, and the importance of specific separation and classification errors.

The proposed penalties were classification-oriented in the sense that they were added based on the classification errors of the S5 system. Further investigation in this direction would be needed, e.g., leveraging more source separation-oriented penalties. The behavior of the metrics will also be assessed on actual S5 system outputs.

## 7. ACKNOWLEDGEMENTS

This research was carried out with the support of the French National Research Agency as part of the CONFLUENCE project number ANR-23-EDIA-0003. Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations.

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