提示词语义密度对AI生成图像信息熵的影响研究——以建筑形象生成为例

摘要：我在雏鹰计划项目中发现，提示词笼统时AI生成的建筑图像多样且不稳定，而详细提示词输出结果更接近我的需求，由此猜想提示词有效信息量越高，生成不确定性越低。研究以建筑形象生成为例，提出语义密度（SD）与图像信息熵（IE）两个量化指标，选取5类建筑，针对每类撰写低、中、高三组提示词，在建筑学长平台生成45张图像并计算灰度熵值。实验显示，SD与IE呈现一定的负相关性（r =  -0.56，p < 0.05），回归方程为ŷ = -0.93x + 8.41，R² = 0.32，说明SD与生成图像不确定性存在某种关联，可解释约32%的熵值变化；分组均值比较提示中密度到高密度的过渡区间存在边际递减的初步迹象。研究为提示词精度影响生成质量提供了量化证据，并建议提示词设计应聚焦核心信息而非堆砌细节。
关键词：语义密度；图像信息熵；提示词；建筑形象生成；生成图像不确定性

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The Impact of Prompt Semantic Density on Information Entropy of AI-Generated Images: A Case Study of Architectural Form Generation

During my participation in the Chuying Program, I observed that vague prompts often produced diverse and even erratic architectural images, whereas detailed prompts yielded outputs more aligned with my expectations. This led me to hypothesise that the higher the effective information content of a prompt, the lower the uncertainty of the generated image. Taking architectural image generation as a case study, this research proposes two quantifiable indicators: Semantic Density (SD) and Image Entropy (IE). Five building types were selected, and for each type, three prompt groups with low, medium, and high semantic densities were composed. A total of 45 images were generated on the Jianzhuxuezhang AI platform, and the grayscale entropy of each image was computed. Experimental results demonstrate a moderate negative correlation between SD and IE (r = -0.56, p < 0.05), with a regression equation ŷ = -0.93x + 8.41. The coefficient of determination (R²) is 0.32, indicating that SD explains approximately 32% of the variation in image entropy. Comparison of group means suggests a preliminary diminishing marginal effect in the transition from the medium-density group to the high-density group. This study provides quantitative evidence that prompt specificity affects generation quality, and recommends that prompt design prioritise core informational dimensions rather than excessive elaboration.
Keywords: Semantic Density; Image Entropy; Prompt; Architectural Image Generation; Uncertainty in AI-Generated Images