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# Impact of Spectral Domain Features for Small Object Detection in Remote Sensing

Urja Giridharan<fnref n="1" />, Neeraj Ramprasad<fnref n="2" />, Sukanta Roy<fnref n="2" />, and S. N. Omkar<fnref n="2" />✉

omkar@iisc.ac.in

**Abstract.** Remote sensing is a vital technique for detecting and monitoring the physical characteristics of an area from a distance: typically, from an aircraft or satellite. Accurate object detection in remote sensing images is crucial since security, transportation, environmental monitoring, and rescue applications in the military and civilian sectors demand comprehensive, precise analysis and utilization of these images. Despite recent advances, small object detection in satellite images is challenging due to the lack of information raised from the area covered by small objects in the image. To address the problem of small object detection, this paper discusses the importance of feature space analysis. The need for distinctive feature space is equally important along with the choice of the model architecture. Focusing on feature space analysis, deep learning is used for the extraction of the granularity of data. Further, spectral context is combined with spatial features to reinforce feature information and thus, enhance the detection. Our strategy involves comparing two units: the Fourier transform unit and the Wavelet packet transform unit to extract spectral features. These units are placed in the EfficientDet to enhance the feature space and assist small object detection by providing context. Three models were trained and tested on DIOR dataset, which is a publicly available dataset. The intuition of adding the transform units to the existing model has shown a remarkable improvement of 20% in the mAP. With limited changes in the number of parameters and without much hyper parameter tuning, the mAP shows improvement. Initially an experiment was conducted on a small custom dataset to test the hypothesis of the impact of feature space in object detection and the models containing the transform units showed an improvement of 4% in the mAP.

**Keywords:** Small object detection · Remote sensing · Fourier transform · Wavelet packet transform

## 1 Introduction

Remote sensing involves obtaining the physical characteristics of an area without requiring proximity. It allows the users to visualize, and analyse the objects and features under observation. It is crucial for collecting a lot of data from dangerous and inaccessible locations. For instance, it is significant for the detection of illegal mining activities, helping

<footnote n="1">¹ Ramaiah Institute of Technology, Bengaluru, India</footnote>

<footnote n="2">² Department of Aerospace, IISc, Bengaluru, India</footnote>
humanitarian teams and contributing to monitoring and verifying conflict zones. Many fields use remote sensing technologies, including: GIS remote sensing to collect, store, and analyse data from any location on Earth, research of natural disasters, monitoring of the environment at mining sites – the data produced by remote sensing can provide information on changes to surface water and land cover, precision agriculture, urban planning, etc. Object detection in optical remote sensing is a technique for locating instances of objects in aerial or satellite images.

In remote sensing imagery small objects are quite common as images are captured from a bird's eye view. The advancement of deep learning has paved the way for remarkable performance in generic object detection. These existing object detectors can precisely detect large objects with high resolution. However, these detectors pose enormous difficulties for detecting small objects as it is challenging to extract information of small objects with low resolution and noisy features. For instance, in a 6000 × 6000 image, objects of size 50 pixels are incredibly small thus presenting a major challenge for generic object detectors. Due to the pooling layer in deep neural networks the small objects cannot retain effective features. Objects in remote sensing imagery usually have complex backgrounds, thus exacerbating the accurate detection of small objects. It is crucial to explore ways to achieve high precision remote sensing object detection. Intuitively, one could build bigger and deeper models to improve accuracy, but this comes at a very high computational cost. Furthermore, pruning can be used to condense larger models, but it is a multi-stage process, and there will always be some accuracy loss, no matter how slight it is.

However, experiments show that learning in the frequency domain achieves higher accuracy than the conventional spatial down sampling [13, 27]. Spectral domain features provide general frequency-domain metrics on the data and provide contextual information. Furthermore, they show that introducing spectral features to spatial domain improves semantic understanding of the object detection model thus improving the performance of the model without significantly increasing the computational cost.

This paper explores the impact of spectral domain features for small object detection in remote sensing by integrating them with a convolutional neural network architecture. We have chosen the EfficientDet model [12] as our CNN architecture because of its compound scaling strategy that scales the resolution, depth, and width of all backbone, feature, and box/class prediction networks. Multiscale feature fusion is quick and easy due to a weighted bi-directional feature pyramid network which offers superior cross-scale feature fusion capabilities. It is a simple and effective network that introduces weights to determine the relative relevance of various input features, since features at different resolutions have different contributions to the output features. In comparison to other object detectors, EfficientDet has the advantage of using fewer parameters and floating-point operations (FLOPs). However, experiments show that the model performs poorly when trained to detect small objects. In an attempt to improve the accuracy of the model, two types of transform units namely, Fourier transform and Wavelet transform have been integrated with the EfficientDet model architecture and studied individually and our experiments show an enhancement in mAP.
# 2 Related Works

## 2.1 Object Detection

There are two primary subcategories of deep learning-based object detection: one-stage and two-stage approaches. In the Two-stage approach, a set of regions of interest are proposed by a select search or regional proposal network in the first stage. Classification and location regressions are run on the ROIs produced in the previous stage. This includes R-CNN, Fast R-CNN, Faster R-CNN [1–3]. One-stage techniques produce object detection without generating any object proposals. They perform detection directly over a large sample of locations. The object detection is treated as a simple regression task-SSD, YOLO [4, 5]. These pipelines are effective for learning discriminative features on large objects with high resolution and distinct appearance. However, they typically fail to recognize extremely small objects because rich representations are challenging to learn and therefore ineffective at multi scale object detection.

## 2.2 Multi-scale Object Detection

Deep learning methods have progressed tremendously in recent years, allowing networks to address the challenge of multi-scale object detection. Furthermore, several multi-scale feature fusion techniques have emerged. One of the key developments for this application is the Feature Pyramid Network (FPN) [6].

Feature pyramid network: FPN [6] is used in a Faster RCNN for extracting high level semantic feature maps. The advantage of these networks is that they are good at recognizing small objects since FPNs suggest propagating high level features downward. In the end, this helps detectors pick up small objects because it enhances abstract low-level layers with semantically stronger information that the network has calculated at or near its head.

However, FPN does not effectively use the feature maps to predict appropriate object sizes. Large object proposals are produced in most feature map levels. Further, medium objects and small objects are proposed in the same feature level.

## 2.3 Small Object Detection

RS scenes, in comparison to generic scenes contain smaller objects that are difficult to recognize due to a lack of adequate details and low resolution. Numerous studies have been conducted to address this issue, with the goal of effectively improving the detection accuracy of small objects by incorporating rich context into models.

The recent developments made in small object detection are shown as follows. The Cross-layer attention network [7] obtains important features that are usually lost during down sampling. It includes skipping connections. To improve the feature extraction of small sized objects in remote sensing images an object detection algorithm using super resolution technique is proposed [8]. Another approach [9] involves making target improvements to the BiFPN network. Since the detection of small objects by EfficientDet is poor, improvements to the BiFPN network structure are made by fusing shallow feature maps with rich spatial information using the bidirectional cross-scale connection feature
fusion network. Feature enhancement and feature fusion have been explored and given importance to improve the small object detection's precision. ARSF [10] designs a spatial feature fusion module to improve the features of small objects. Extended feature pyramid network (EFPN) [11] includes a module for feature texture transfer (FTT) to provide reliable details for precise small object detection results.

## 2.4 Spectral Context-Fourier Transform and Wavelet Transform

Experimental results demonstrate that learning in the frequency domain and analyzing the spectra bias preserves image information [13]. Further, it can achieve higher accuracy than traditional spatial down-sampling while also reducing input data size.

Spectral neural networks [14, 15] have been used to efficiently implement non-local receptive fields from a frequency standpoint. According to the spectral convolution theorem [16], every value in the frequency domain is calculated from every value in the spatial domain. As a result, changing a value in the spectral domain can have an impact on all spatial domain data globally. The Fast Fourier Convolution [14] was proposed on the basis of this theorem to investigate an efficient combination of non-local receptive fields and cross-scale fusion with the convolutional unit in the frequency domain for keypoint detection, action recognition and image recognition.

Fast Fourier transform has been utilized to extract key features in an image. Additionally, a series of works have also explored the wavelet transform along with CNNs. Wavelets in wavelet transform are localized waves and can extract local spectral and temporal information. Joan Bruna and Stephane Mallat show that wavelet transforms in CNN create an invariant representation [17]. Moritz Wolter et al. multiscale packet representation for fake image analysis [18]. Their work is based on the theory that the wavelet transforms conserve spatial information to a certain degree. Moreover, wavelets allow us to learn about the spatial organization of differences in the frequency domain. Fortuna-Cervantes et al. proposed a CNN supplemented by 2D discrete wavelet transform. This is used as a feature extraction method [19]. They show that characteristics at low and high frequencies influence CNN performance during training. B. Yu, H. Lu and H. Tao proposed a wavelet packet transform CNN [20] to improve feature learning by introducing a residual learning block. However, to the best of our knowledge, these transforms haven't been integrated with convolutional neural network architectures for small object detection in remote sensing.

Small object detection in remote sensing involves notoriously complex background and low resolution of small objects. Hence, the determination of the characteristics of the objects is difficult. To improve the feature space and the efficiency of extraction of features we hope to explore the possibility of combining spectral features and spatial information and compare the effects of Fourier transform and Wavelet transform on the accuracy of the object detection model. The experiments were conducted using the intuition that adding spectral domain features to spatial domain enhances the feature space by giving additional context thus improving the precision of small object detection. For example: an airplane alone is difficult to recognize in a remote sensing image, but with the addition of its surrounding context (e.g., aircraft carrier, airport, runway), the small airplane detection becomes easier.
# 3 Methodology

## 3.1 Detailed Overview of Our Approach

This paper focuses on the EfficientDet architecture since the goal of combining features is to merge representations of an image at various resolutions and scales. The backbone network EfficientNet represents the features at different levels. In this study we incorporate spectral units to the EfficientDet architecture. These spectral units are introduced after the EfficientNet layer at the multiscale inputs to the BiFPN layer. Since the representation of features at various scales are vital to precisely detect small sized objects the transform units have been placed before the BiFPN layer in order to completely exploit the spectral features as shown in Fig. 1.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Diagram of EfficientDet with Spectral Unit</figcaption></figure>

Figure 1 shows the incorporation of the spectral unit block into the architecture. The extracted feature maps are converted from the spatial domain to the frequency domain by using Fourier transform and Wavelet Packet transform. Experiments were conducted using Vanilla EfficientDet Network (no transform was incorporated), EfficientDet with Fourier Transform Unit and EfficientDet with Wavelet Packet Transform Units.

Experiments were conducted to compare the effect of connecting these units in series and in residual with the BiFPN layer. It was observed that the loss decreased significantly when the spectral units were connected residually as shown in Fig. 1. The details of the implementation are discussed further in Sect. 4.2 under the implementation details section.

We aim to improve the mAP of small object detection without increasing the computational intensity of EfficientDet. The model used in this study is the efficientdet-d0-tf model which is one of the EfficientDet models designed to perform object detection. The experiments in this study have been conducted on two open-source datasets- Birdview vehicles dataset and DIOR dataset. Thus, our experiments involve training three models-EfficientDet, EfficientDet with Fourier Transform units and EfficientDet with Wavelet packet transform units. The details of the fourier transform unit and wavelet transform unit are shown below.
<figure><img src="image_4.png" /><figcaption>Fig. 2. Fourier Unit</figcaption></figure>

## Fourier Transform Unit

Figure 2 shows the structure of the Fourier unit. The goal of the Fourier unit is to convert spatial features into spectral domain, perform global updates on spectral data, and thus transform the data back to spatial format [14].

The core objective of adding a Fourier unit is to learn interaction between spatial locations in the frequency domain. According to the spectral convolution theorem in Fourier theory, there is a huge impact on all of the data when a change in value is made in the spectral domain. The Fourier unit adds value to the detection of small objects by using frequency domain convolution to extract global context as supporting information. The spatial features are extracted from the EfficientNet backbone and further passed into the Fourier unit. The Bi-FPN layer fuses the spectral context with object features at different scales. These features provide a global context thus improving the detection of small objects with complex backgrounds.

## Wavelet Packet Transform Unit

Wavelet transform has excellent localization properties in both frequency and time domains. It is useful to extract local, spectral and temporal features. Wavelet analysis can portray the locality of a signal in the frequency domain thus it can focus on the detail of objects. Wavelets can describe local features that have local extent in a better manner. In Fig. 3, the discrete wavelet packet transform (DWPT) can utilize more information of source image than discrete wavelet transforms (DWT), so it can enhance the feature space. The packet approach provides the opportunity to decompose high frequency bands in fine detail. In comparison with DWT, the wavelet packet analysis gives better control on the frequency resolution for the decomposition of the signal.
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** 2D wavelet packet transform [20]</figcaption></figure>

Every channel is taken as a separate feature set, which aids in improving the feature space at each level. The wavelet packets are concatenated with the convolution filters. For the feature fusion experiments, we use wavelet packets with three levels and we choose the Daubechies 5- wavelet representation. Incorporating wavelet packets into a pixel-CNN improves the outcome.

# 4 Experiments

## 4.1 Dataset

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Birdview Vehicles dataset-small and large bird view vehicles</figcaption></figure>

The experiments were conducted on two open-source datasets. The initial experiment was conducted on a small dataset which is a birdview vehicles dataset [28] This dataset consists of 2 classes- small and large vehicles as shown in Fig. 4. It comprises 1111
<figure><img src="image_7.png" /><figcaption>Fig. 5. DIOR dataset [21]</figcaption></figure>

images in the train set and 249 images in the validation set. Experiments were conducted on this dataset which showed promising results. The implementation details are given in Sect. 4.2.

The second experiment is then conducted on the DIOR dataset [21] which is a publicly available dataset consisting of remote sensing images for object detection as shown in Fig. 5. The dataset contains 23,463 remote images. It contains 20 classes which are-Airplane, Airport, Baseball field, Basketball court, Bridge, Chimney, Dam, Expressway service area, Expressway toll station, Golf field, Ground track field, Harbor, Overpass, Ship, Stadium, Storage tank, Tennis court, Train station, Vehicle, and Windmill. DIOR dataset is sourced from Google Earth with an image size of 800x800 pixel. The validation dataset consists of 5000 images.

## 4.2 Implementation Details

All experiments were implemented using Pytorch 1.12.1 and the models were trained using Google Colab Pro. The EfficientDet model is pre-trained on the MSCOCO dataset, which is a large dataset that comprises 170 image classes along with annotations spread across 100,000 images. In this study the EfficientDet-d0 model is used which has a COCO mAP (0.5:0.05:0.95) of 31.95%. The Focal loss was chosen as the loss function to train the object detection model, since it handles the class imbalance problem by assigning weights to harder easily misclassified examples (e.g., background with noisy texture or partial object or the object of our interest). In our approach the spectral units are introduced after the EfficientNet layer at the multiscale inputs to the BiFPN layer. The connection of the spectra units in the EfficientDet model is discussed below.
## Spectral Unit

Experiments were conducted on the small dataset to compare the performance of the models when the units are connected in series and when they are connected in a residual manner with the BiFPN layer.

<figure><img src="image_8.png" /><figcaption>Fig. 6. Spectral unit connected in series</figcaption></figure>

Initially, both the spectral units were connected in series as shown in Fig. 6 with the BiFPN layer at every level of the EfficientDet network such that the spatial domain features $F_s$ are transformed to the spectral domain features $F_f$. The loss was observed after training the models for 40 epochs. However, experiments showed only a slight decrease in the loss. Thus, another approach was considered to incorporate the spectral units to the model.

<figure><img src="image_9.png" /><figcaption>Fig. 7. Residual connection of the Spectral unit</figcaption></figure>

The units were then connected in a residual manner as shown in Fig. 7 such that the spatial domain features $F_s$ are transformed to the spectral domain features $F_f$ and concatenated back as a residual link, resulting in frequency aware features $F_{fa}$. The models were again trained for 40 epochs on the small dataset. This method of connection resulted in a significant decrease in the loss of both the models. Intuitively, we understand that the addition of spectral features gives context to the spatial domain thus enhancing the feature space. Hence, the introduction of frequency domain to spatial domain improves the small object detection's precision.

The implementation of the training of the 3 models-Vanilla EfficientDet, EfficientDet with Fourier transform unit and EfficientDet with wavelet transform unit is as shown below.

## Implementation on Custom Dataset

First our hypothesis of adding spectral context to the spatial domain was tested by conducting an experiment on a small custom dataset. The training loss was compared by
introducing the spectral units in series and as residual blocks at the multi scale inputs to the BiFPN layer. It was observed that the loss decreased when the units were connected as a residual block. We train the three models for 40 epochs. The pretrained weights on ImageNet are used for the first 30 epochs to reduce the time of training. The model was trained by freezing all the layers but the head. Since our approach involves changes in the model, the weight from the 30th epoch is further used for the last 10 epochs where the model is trained from scratch. The initial learning rate is 1e-3. The model was further evaluated on the validation dataset and the mAP was noted. Since, a significant improvement was noticed in the mAP after the addition of spectral units we further conducted an experiment on the large publicly available DIOR dataset.

Implementation on DIOR Dataset

The three models are trained on the DIOR remote sensing dataset. Due to the size of the dataset, the pretrained weights on ImageNet are used for the first 30 epochs. The models are trained by freezing all the layers but the head. The weight at the 30th epoch is saved and further used for the last 10 epochs where the model is trained from scratch. The initial learning rate is 1e-3. The model is then evaluated on the validation dataset and the mAP is observed.

5 Results

The following results have been obtained from the experiments conducted. The mean average precision of the three models- Vanilla EfficientDet, EfficientDet with Fourier transform unit and EfficientDet with wavelet packet transform unit were noted. The results of mAP at IOU = 0.5 are shown below.

<table><caption>**Table 1.** Results on birdview vehicles dataset</caption><thead><tr><th></th><th>EfficientDet</th><th>EfficientDet with Fourier transform Unit</th><th>EfficientDet with Wavelet packet transform Unit</th></tr></thead><tbody><tr><th>Mean Average Precision</th><td>73.9</td><td>77.1</td><td>76.0</td></tr></tbody></table>

Table 1 shows the evaluation results of the models trained on the bird view vehicles dataset. The hypothesis that the addition of spectral context to spatial domain improves the precision of object detection is seen in this experiment. It can be seen that by adding the spectral transforms the mAP is improved by 4% with Fourier transform unit and 3% with wavelet packet transform unit.

Table 2 shows the results obtained after training the models on the DIOR dataset. It can be observed that by adding spectral context the mAP is enhanced by 20% in the case of Fourier transform. The addition of frequency domain analysis of the feature space improves the feature space thus increasing the relative mean average precision by 66%.

A significant change in the mAP is observed without any computational overhead and fine tuning (Fig. 8).
<table><caption>**Table 2.** Results on DIOR dataset</caption><thead><tr><th></th><th>EfficientDet</th><th>EfficientDet with Fourier transform Unit</th><th>EfficientDet with Wavelet packet transform unit</th></tr></thead><tbody><tr><th>Mean Average Precision</th><td>33.6</td><td>53.3</td><td>50.0</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Graph representing the comparison of the results</figcaption></figure>

The introduction of spectral context enhances the mAP significantly and this is visualized using a bar graph in Fig. 2. The graph compares the final inference results (mAP) from the three models.

Global features are useful for describing the entire image to generalize the object while the local features represent specific points in the image. The impact of global context is more crucial than local context. Although the results of both the transforms are comparable, the Fourier transform performs slightly better due to the fact that it provides global context. Wavelet transform on the other hand provides local spectral context.

# 6 Conclusion

Remote sensing is crucial for the detection of illegal mining activities, helping humanitarian teams and contributing to monitoring and verifying conflict zones. Despite recent advances, small object detection in satellite images is challenging. In this paper, we propose a methodology on how to improve the accuracy of small object detection, by including contextual information via transformations to the frequency domains. The results show that there is an increase of mAP by 20% upon the addition of spectral domain features. A good feature space is essential for object detection; hence we explore feature space analysis by adding Fourier transform unit and wavelet packet transform unit in
the model architecture-EfficientDet. A further analysis is done on the impact of global features. In the future, these units can be incorporated in the state-of-the-art models. It can be hypothesized that the mAP can be improved to 75%, thus boosting the precision of small object detection.

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