# What distance metric can I use for comparing image features like elongation and solidity of each image?

What distance metric can I use for comparing image features like elongation and solidity of a contour of each image? Except Least Square and without using a support vector machine because i do not know at which class images belong.

-

Have you tried using the first two eigenvectors of the contour matrix (or its covariance matrix) as a measure for elongation? – Junuxx Feb 27 at 9:59

## 1 Answer

If I understood you correctly, each contour is described by a 2-element feature vector $f = [e, s]$, where $e$ is elongation and $s$ is solidity.

In that case, you might want to try the Mahalanobis distance, which is defined as follows: $$d(f_1, f_2) = \sqrt{(f_2 - f_1)C^{-1}(f_2 - f_1)}$$ where $f_1$ and $f_2$ are the feature vectors that you are comparing, and $C$ is the covariance matrix of your data set.

-
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9420327544212341, "perplexity_flag": "head"}