## 3 Proposed Method
### Multimodal Decision-Level Fusion Approach
#### 3.3.2 Score Fusion Strategy  
To ensure prediction accuracy, the network typically receives only a single localized block when classifying and predicting fingermark images. This input strategy, however, can introduce randomness and reduce the robustness of the results. For this reason, we propose the multi-input score fusion strategy. We use a sliding window in the image preprocessing step to intercept multiple local blocks and feed them into the network. This results in multiple independent prediction probabilities, which we combine using the score fusion  
Figure 4: Different classification strategies. Where (**a**) represents Original classification strategy, (**b**) represents Improved classification strategy and (**c**) means Multi-probability labeling strategy. method to calculate the final classification prediction probability, as shown in Figure 5. The final classification prediction probability of the input fingermark image is determined by utilizing the voting results of multiple prediction inputs. Equation (3) presents the calculation formula for the classification prediction probability. \[\text{P}_{\text{predict}}=\frac{1}{\text{N}}(\text{P}(\text{y}_{1}|\text{x}_{1} )+\text{P}(\text{y}_{2}|\text{x}_{2})+\ldots+\text{P}(\text{y}_{\text{N}}|\text {x}_{\text{N}}))=\frac{1}{\text{N}}\sum_{i=1}^{\text{N}}\text{P}^{\text{y}_{i} }(1-\text{p})^{1-\text{y}_{i}} \tag{3}\]  
where \(\text{P}(\text{y}_{i}|\text{x}_{i})\) denotes the prediction score of the current local block, \(\text{x}_{i}\) denotes the current local block input to the network for prediction, \(\text{y}_{i}\) is the prediction label of the corresponding local block output by the network, and \(\text{P}\) is the confidence level corresponding to \(\text{y}_{i}\). However, considering that the local blocks obtained from the sliding window intercepts have an uneven texture distribution and are affected by signatures, the score fusion strategy with equal weights cannot reflect individual differences. The effective area contained in the localized block has large individual differences, and too large a background area will lead to performance degradation of the detection algorithm. In addition, the region impacted by the signed lines will affect the performance of the detection algorithm, i.e., the proportion of the signed lines in the local block is negatively correlated with the credibility of the detection results of the local block. Therefore, in this paper, we design the score fusion method based on the quality weight of fingermark localized blocks and propose the quality score calculation method based on the effective region and the proportion of signed lines, and the calculation formula is shown in Equation (4):  
\[\text{Q}=\sigma\text{Q}_{\text{ROI}}+\tau\text{Q}_{\text{Signature}}=\sigma \frac{1}{\text{w}\times\text{h}}\sum_{i=1}^{\text{w}}\sum_{j=1}^{\text{h}} \varepsilon\big{[}\text{P}(i,j)-\text{P}_{\text{ROI}}\big{]}+\tau\frac{1}{ \text{w}\times\text{h}}\sum_{i=1}^{\text{w}}\sum_{j=1}^{\text{h}}\varepsilon \big{[}\text{P}(i,j)-\text{P}_{\text{Signature}}\big{]} \tag{4}\]  
where \(\varepsilon(\text{t}-\text{t}_{0})\) is the step function whose value is 1 at \(\text{t}-\text{t}_{0}\geq 0\) and 0 vice versa; \(w\) and \(h\) are the width and height of the localized block, respectively; \(p(i,j)\) is the pixel value of the current coordinate; \(\text{P}_{\text{ROI}}\) is the threshold for distinguishing between the valid area of the fingermark and the blank background, \(\text{P}_{\text{Signature}}\) is the threshold for distinguishing between the signed line and the valid area; and \(\sigma\) and \(\tau\) are correction coefficients for effective region  
Figure 5: Score fusion via the multiple input strategy. Which shows a fingermark with Chinese signature. weights and signed line weights.