*3.2. Event-to-Frame Transformation*

In this method, the generation of event frames follows that of Event Map instead of TS or SAE. Since TS- or SAE-based event-frame-generation method involves exponential computing, it is thus not used to reduce computing complexity.

Event-to-frame transformation follows two modes as shown in Equation (2): One is collecting a constant number τ*FixNum* events. The events are projected on the image plane to form a binary image. Absence and presence of events within the temporal window are expressed by 0 and 1, respectively.

Another way is by the timestamps of intensity images. If one intensity image has been received, the events between the timestamp of last frame (intensity frame or event frame) and current timestamp, which is represented by τ*FixTime*, will be collected. That is, each intensity image has an attached event frame. This will cause one potential problem: If the number of events is too small, the generated event frame will be too sparse for reliable feature tracking. However, this situation will be alleviated by the following integration from intensity image:

$$\Pi(\mathbf{x}, \mathbf{y}) = \begin{cases} 1 & \text{if } \operatorname{event}(\mathbf{x}, \mathbf{y}, t) \in \mathsf{\tau}\_{\text{FixNum}} \text{ or } \mathsf{\tau}\_{\text{FixTime}}\\ 0 & \text{otherwise} \end{cases} \tag{2}$$

#### *3.3. Affine Transformation-Based Multiple Hypothesis Testing for Batch Processing (MHT-BP)*

The work of [19] proposed five hypotheses purely based on event flow, which are Null, East, North, West, and South hypotheses. Firstly, a template and a model are generated from a time window on event flow. Then the alignment score that quantifies their differences is calculated to guide the selection of the above-mentioned five hypotheses.

Inspired by the work of [19], a batch processing-based multiple hypothesis testing using four-parameter affine transformation model (MHT-BP) is proposed to improve feature-tracking efficiency. Compared with the five hypotheses in [19], the four-parameter affine transformation model explores more hypotheses to improve matching accuracy. Moreover, batch processing is conducted to improve efficiency.

Since with the above-mentioned data stream, the possible minimal "frequency: of event frames is equal to that of intensity frame, the difference between consecutive frames is small enough for patch comparison. The small feature motions bring three benefits to improve efficiency and accuracy: (1) neighboring areas near features can provide supporting regions to make multiple hypotheses; (2) a set of features are able to share the same affine transformation, and therefore, batch processing can be conducted to improve efficiency; and (3) the search range of four parameters in the affine transformation model can be small.

The four-parameter affine transformation model is applied to generate multiple hypotheses. α, θ, Δx, and Δy represent the variation on scale, rotation, and translation on X and Y, respectively. The four parameters between affine transformation are shown in Equation (3).

$$\mathbf{T}\_{Aff} = \begin{pmatrix} \alpha \cos \theta & -\alpha \sin \theta & \Delta \mathbf{x} \\ \alpha \sin \theta & \alpha \cos \theta & \Delta \mathbf{y} \\ 0 & 0 & 1 \end{pmatrix} \tag{3}$$

The illustrative example of MHT-BP is illustrated in Figure 3 given two event frames *Ft* and *Ft*+1. A patch on *Ft* containing a set of features are selected with the four-parameter affine transformation model. The patch is transferred to generate multiple hypotheses; that is, each hypothesis corresponds to an affine transformation. After Gaussian blur, their differences are indicated by sum of absolute differences (SAD). The affine transformation model with minimum distance is chosen to establish correspondences between the two patches. This process will go on until all the features are involved.

**Figure 3.** Illustrative example for multiple hypothesis testing with four-parameter affine transformation model.
