Image Triangulation Using the Sobel Operator for Vertex Selection

TL;DR

An image triangulation algorithm in Python is discussed that utilizes Sobel edge detection and point cloud sparsification to determine final vertices for a triangulation, resulting in the creation of artistic triangulated compositions.

Abstract

Image triangulation, the practice of decomposing images into triangles, deliberately employs simplification to create an abstracted representation. While triangulating an image is a relatively simple process, difficulties arise when determining which vertices produce recognizable and visually pleasing output images. With the goal of producing art, we discuss an image triangulation algorithm in Python that utilizes Sobel edge detection and point cloud sparsification to determine final vertices for a triangulation, resulting in the creation of artistic triangulated compositions.

Figures (7)

• Figure 1: (Left) Original image before processing. (Right) Image after converting to grayscale.
• Figure 2: The image convolution process, which produces a new image by taking a weighted sum of each original pixel and its surrounding pixels. For the pink pixel $I_{xy}$, $H_{xy}=-b-d+5e-f-h$.
• Figure 3: Image after (Left) sharpening with Eq. \ref{['eq:sharpeningKernel']} kernel, (Right) applying the Sobel operator.
• Figure 4: (Left) Triangulation of image. (Right) Final colored image triangulation.
• Figure 5: Differences in final image triangulation depending on threshold to select pixels.