To promote the generalization ability of breast tumor segmentation models, as well as to improve the segmentation performance for breast tumors with smaller size, low-contrast amd irregular shape, we propose a progressive dual priori network (PDPNet) to segment breast tumors from dynamic enhanced magnetic resonance images (DCE-MRI) acquired at different sites. The PDPNet first cropped tumor regions with a coarse-segmentation based localization module, then the breast tumor mask was progressively refined by using the weak semantic priori and cross-scale correlation prior knowledge. To validate the effectiveness of PDPNet, we compared it with several state-of-the-art methods on multi-center datasets. The results showed that, comparing against the suboptimal method, the DSC, SEN, KAPPA and HD95 of PDPNet were improved 3.63\%, 8.19\%, 5.52\%, and 3.66\% respectively. In addition, through ablations, we demonstrated that the proposed localization module can decrease the influence of normal tissues and therefore improve the generalization ability of the model. The weak semantic priors allow focusing on tumor regions to avoid missing small tumors and low-contrast tumors. The cross-scale correlation priors are beneficial for promoting the shape-aware ability for irregual tumors. Thus integrating them in a unified framework improved the multi-center breast tumor segmentation performance.

The irregular strip packing problem (ISP), or often called the nesting problem, is the one of the representative cutting and packing problems that emerges in a wide variety of industrial applications, such as garment manufacturing, sheet metal cutting, furniture making and shoe manufacturing [Alvarez-Valdes et al., 2018, Scheithauer, 2018]. This problem is categorized as the two-dimensional, irregular open dimensional problem in Dyckhoff [1990], Wäscher et al. [2007]. Given a set of pieces of irregular shapes and a rectangular container with a fixed width and a variable length, this problem asks a feasible layout of the pieces into the container such that no pair of pieces overlaps with each other and the container length is minimized. We note that rotations of pieces are usually restricted to a few number of degrees (e.g., 0 or 180 degrees) in many industrial applications, because textiles have grain and may have a drawing pattern. Figure 1 shows an instance of the ISP and a feasible solution. The first issue encountered when handling the ISP is how to represent the irregular shapes. In computer graphics, the irregular shapes are often represented in two models as shown in Figure 2: the vector model represents an irregular shape as a set of chained line and curve segments forming its outline, and the raster model (also known as the bitmap model) represents an irregular shape as a set of grid pixels forming its inside.