# Spatial Domain-Based Nonlinear Residual Feature Extraction for Identification of Image Operations
## 1 Introduction  
Currently, forgeries of digital images are widely propagated, and it is expected that tampered images will be used more and more in society, including in social media and even scientific discovery. This will cause a serious impact on political and social stability. At the same time, while postprocessing techniques and operations for use with digital images are developing rapidly, the imperceptible modification of digital images is becoming easier. Therefore, ever-increasing attention is being paid to digital image forensics, including detection of forgery and postprocessing operations. To date, many approaches regarding image forensics have been proposed, such as tracking the history of JPEG compression [1; 2; 3; 4]; revealing the image operations, including contrast enhancement [5; 6], resampling [7; 8; 9; 10], and median filtering [11; 12; 13; 14]; detecting the image splicing operations [15; 16], revealing frequency domain filtering [17]; and identifying image forgery [18; 19]. However, most of these state-of-the-art studies have simply considered specific operations. On the other hand, some of the approaches only perform binary classification. In [1; 2; 3; 4], the authors proposed methods of detecting history of JPEG compression and revealing artifacts caused by image coding. The methods were based on blocks. In [6], [PERSON] and [PERSON] proposed detecting the occurrence of digital image modification according to contrast enhancement operations in a blind way. In [7], [PERSON] and [PERSON] proposed detecting the resampling traces and interpolations based on a derivative operator and the radon transformation. In [20], [PERSON] and [PERSON] proposed detecting forgeries in digital images using a deep learning method. In [21], two-class 3D-convolutional neural network (3D-CNN) classifiers were employed for video copy detection. However, in most cases, the features show low feasibility andreasonability, especially when the processing types of the detected images are unknown. For example, if we fed a median-filtered image into a classifier to detect the histogram equalization, it could be classified as a histogram-equalized image or an original image. Either result would be wrong because the feature employed in this approach is specially designed for detecting histogram equalization. Similarly, the accuracy of identifying other image operations will drop significantly if we apply the same classifier. Therefore, an effective forensics approach that can identify various image operations simultaneously is essential and of great importance. Recently, in [22], a method based on a spatial rich model (SRM) feature was proposed. The SRM was proposed to be used as a steganalysis feature by [PERSON] et al. [23]. Multiple nonlinear and linear filters were employed to generate residuals, and then the high-order features were extracted and merged into the SRM features. Experiments were conducted to select the multiple sets of filters, and they can be used under different models to extract the residual information from the image. In [22], [PERSON] et al. proposed reducing the dimensionality of the SRM features. Afterward, they applied an ensemble classifier [24] for classification of the various common image postprocessing operations. Experimental results showed that this scheme performed better than most of the related state-of-the-art works; however, there was an obvious downtrend when the size of the observed images was decreased. Furthermore, features in this work were manually designed, and thus they might not be effective enough for identifying the various image operations because of the high complexity. The ensemble classifier [24] is a multiclassifier ensemble method that utilizes the complementary relationships of the classifiers to improve the generalization ability effectively, and it can be used to work with high-dimensional features with significantly lower training complexity.