Page - 184 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

preserving visual information that is important for human perception up to high levels of the pyra- mid. It is known that standard image pyramids such as Gaussian and Laplacian pyramids as well as hierarchical representations based on these concepts eliminate noise in the image due to the repeated smoothing operation [6]. However, since regions showing noise may also be consider as highly tex- tured regions this may not be the case for SCIS. Therefore, we analyze the noise robustness of SCIS in thispaper. The rest of the paper is structured as follows: A short introduction to the SCIS algorithm is given in Section 2. Its robustness to noise is tested in experiments presented in Section 3. Results of these experimentsarediscussed inSection4.Section5. concludes thepaperandgivesanoutlook to future work. 2. StructurallyCorrect ImageSegmentation The“structurallycorrect imagesegmentation” (SCIS)algorithmwasfirstpresented in [3]. Although, SCISisbasedonLBPsitdoesnotusehistograms. Thishierarchicalsegmentationapproachconstructs an irregular graph pyramid (sequence of reduced graphs), by iteratively identifying and removing re- dundant structural information, andmerging regionswith the lowestdissimilarityfirst. The SCIS algorithm represents an image as a directed acyclic graph. Each vertex corresponds to a pixel, a superpixel or a region, and each edge corresponds to an adjacency relationship between two pixels, superpixelsor regions. Aftermergingneighboringverticeswithequalgrayscale-/colorvalues, it is possible to assign each edge a direction, and thus describing the relationship between adjacent vertices as strict inequality relationships. As a result, this merging induces a strict partial order onto the vertices of the image graph. This ordering of the vertices is not a total ordering, because not all pairs of vertices are comparable by following monotonically increasing or decreasing paths. An edge is said tobe”structurally redundant”, if the removalof this edgedoesnotbreak the reachability property of the graph. The SCIS algorithm identifies most of these redundant edges in a fast manner by means of a primal and dual topological LBP classification (see [4] for more detailed information) and removes them. SCIS (see Algorithm 1) employs this idea, mentioned as simplifying the structure in algorithm 1 (line 5-8). Structurally redundant dual edges are determined and removed. Subsequently, regions with the lowest dissimilarity are merged. In the case of grayscale images, the absolute region in- tensity difference d(x,y) = |g(x)−g(y)| is used, wherex and y are two regions, and g(x) is the Algorithm1 structurallycorrect imagesegmentation (SCIS) input: 2Dimage output: combinatorial pyramid 1: k :=0 2: initializebase levelC of combinatorial pyramid 3: C′ := removedual saddles inC 4: C0 :=mergeplateaus inC′ 5: repeat 6: k :=k+1 7: simplify structure incurrent levelCk 8: untilCk=Ck−1 184