###### Abstract
New disks were expanded by user-specified fractions of the parent disk's minimal radius. [PERSON] et al. (2006) developed a feature expansion algorithm to find high-quality depth maps. They suppressed outliers through a combination of intelligent image selection at per-view and per-pixel levels, and a sequential expansion strategy based on a priority queue. Their algorithm was capable of addressing the extreme changes in lighting, scale, clutter, and other effects in large online-community photo collections. [PERSON] et al. [PERSON] et al. (2006) arrived at a patch-basedfeature expansion algorithm, Patch-based Multi-View Stereopsis (PMVS), which consisted of three key steps: match, expand, and filter. In the first step, sparse features were matched using Harris and difference-of-Gaussians operators. The last two steps iterate \(n\) times to spread the initial matches to nearby pixels and obtain a dense set of patches. From [PERSON] et al. to [PERSON] et al., in addition to the improvements in performance, the three key steps in the feature expansion algorithm framework became increasingly clear. The last step--the filtering of outliers--was not fully implemented until [PERSON] et al. As a result, [14; 15] had to adopt greedy or best-first sequential strategies, as shown in Table 1, to suppress outliers. With the filtering of outliers based on visibility and weak neighborhood regulation, [16] was able to expand all the patches with the same priority. PMVS is now regarded as a state-of-the-art MVS algorithm. Nevertheless, there is still a lot of room for improvement in the framework and in the key steps of the feature expansion algorithm. For example, the assignment of the next expanding point still relies on a reference image, i.e., the assignment is conducted in a local coordinate system, rather than occurring directly in a fixed-world coordinate system. This paper presents a novel MVS algorithm based on homogeneous direct spatial expansion (MVS-HDSE). It extends the framework of the feature expansion algorithm by introducing an additional step for initial value modification utilizing already-expanded neighbor points. It also makes important improvements to existing steps in order to attain high accuracy and completeness while maintaining high efficiency. Briefly, the proposed algorithm adopts many unique measures, including:  
1. Initial seed point extraction by the DAISY descriptor: in the seed point extraction step, the high-performance DAISY descriptor was introduced to increase the number and accuracy of seed points. Like Multi-View Reconstruction Environment (MVE) systems [26] and Visual Structure From Motion (VSFM) systems [27], the proposed algorithm can also get initial sparse seed points via SFM [4], which first detects Scale-Invariant Feature Transform (SIFT) [28] feature points in images and then matches the points between pairs of images. Seed points result from successfully-matched points following triangulation principles. However, the accuracy and number of seed points might reduce greatly due to mismatches or match failure. When the high-performance DAISY descriptor is used, the number of initial seed points might be increased multiple times, which is very helpful for reconstruction completeness and efficiency. This is because feature matching is now replaced by the DAISY descriptor's similarity searching. The former is conducted between limited pairs of existing feature points, whereas the latter is performed along epipolar lines. 2. Homogeneous direct spatial expansion: in the expansion step, all 3D seed points are given with the same priority, i.e., every seed point is simultaneously expanded to nearby 3D points. This strategy is especially suitable for parallel computation, since it is neither necessary to keep a seed priority queue for sequential growth [14], nor to grow a new seed point until it cannot grow anymore [15]. Instead, every seed point is directly expanded in 3D space with a small step along its tangent plane, and the world coordinates of the expanded 3D points are recorded directly.