# Objects, Holes and their Features Objects and holes are both represented by the class [`ECodedElement`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html), so they are managed in the same way and share the same functions. Use [`IsObject`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a5d21b5a22b34fc2cd82488b0f1b4d217) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a0ebc5538599a5b4c6e7e7293ea99700e) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a26f021cf200ca5320a57cecf88c35a59) or [`IsHole`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#aa6d8220200a8c2f3cce9b923921ec73f) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a03f461974c490243e74b91de72b23083) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#adb4ced35f83b7ff972e34914a923ec4e) to determine the type of the coded element. ## Holes Construction A hole is a set of connected pixels that is entirely surrounded by a parent object. A hole has no child. Objects inside a hole are considered to be separate objects. To get the holes of a specific object, use [`GetHoles`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#aa2085dfe54be939b0bed6dd0e108b692) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ae25a5203bb8068cbfb2ca3470c537294) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a42b90c7fee4f2c8c9aa483021a4ba894). With an [object selection](selecting_and_sorting_blobs.html.md#easyobject-object-selection), you can also add the holes of all the objects of a coded image using [`EObjectSelection::AddHoles`](../../../doxygen_cpp/classeVision_1_1EObjectSelection.html#a55f2e9237cdf39145ce62d557ac8c2b7) [_.NET](../../../doxygen_cs/classeVision_1_1EObjectSelection.html#ac4dae66d3b07ef813cfb121fc15f6785) [_Python](../../../doxygen_python/classeVision_1_1EObjectSelection.html#a07d8629e8b357e512995473c4ed976dd) and add the holes of all the objects of the selection using [`EObjectSelection::AddHolesOfSelectedObjects`](../../../doxygen_cpp/classeVision_1_1EObjectSelection.html#a083e0ed9a47e539652b5516c92851c0d) [_.NET](../../../doxygen_cs/classeVision_1_1EObjectSelection.html#a04c10072ada31dbdeac214f7226b0a91) [_Python](../../../doxygen_python/classeVision_1_1EObjectSelection.html#aa6141dd3e4f859be4a8c8ff4636c4749).  #### SEE ALSO See the [code snippets](../../../resources/code_snippets/matching_and_measurement/easyobject/holesextraction.html.md) showing how to extract the holes from the objects. ## Features **EasyObject** can compute various features for each object and use these features for filtering or sorting. There are two main categories of features: * Cacheable features that will be computed only once on the first invocation. These features corresponds to methods prefixed with `Get` in C++ or properties in C# and Python. * Non-cacheable features that will be reevaluated at every invocation. These features corresponds to method prefixed with `Compute`. * Note that these features usually requires an additional parameter or are slower to compute. Most features will be expressed in the [frame of reference](../../basic_operations/frame_and_alignment.html.md) used when *encoding* the image. However, some features are computed at the pixel level. In the tables below, the frame of reference is indicated in the corresponding column: - *Frame* means that the result is expressed with regard to the frame that was used when *encoding* the image. - *Pixel* means that local pixel coordinates are used, irrespective of the frame. ### Gravity Center | Feature | Method | Data type | [Frame of reference](#easyobject-objects-features-frame) | |------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------| | Gravity center

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(X and Y) | [`GetGravityCenter`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a66e421b1ce6588c1cf572d9da8939fa2) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#aecb5edc985078821d437178e8b85af24) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a6344670e34401f569da8ff77864fce44)

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[`GetGravityCenterX`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ac02576be08fb43b5cd74a6ab4e0c7e24) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a6e89b5d85f08867bfcbdc520cc798e90) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a52939cece9828e1a11198f35d4709d0c)

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[`GetGravityCenterY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ad2530327fce961ca7d6a918859b37f75) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a9e2d1fc6cf13ae7dec82f7fde8e51a81) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#afa46d8fddaaaf40d6b4bc8e1be2604b1) | [`EPoint`](../../../doxygen_cpp/structeVision_1_1EPoint.html) [_.NET](../../../doxygen_cs/structeVision_1_1EPoint.html) [_Python](../../../doxygen_python/classeVision_1_1EPoint.html)

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Float | frame | | Weighted gravity center

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(X and Y) | [`ComputeWeightedGravityCenter`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a5da623dd37476c23540fb904b5fd946e) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a270ccad2a553b938b8fa8061995d520f) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a311f49724aa212608ece30cb32c7a1e3) | [`EPoint`](../../../doxygen_cpp/structeVision_1_1EPoint.html) [_.NET](../../../doxygen_cs/structeVision_1_1EPoint.html) [_Python](../../../doxygen_python/classeVision_1_1EPoint.html) | frame |  The **gravity center** is the average of the coordinates, expressed in a frame of reference, of all the pixel of the blob: $$ G = \frac{1}{N} \sum_{i=1}^N p_i $$ The **weighted gravity center** requires an input image and is the average of the coordinates, expressed in a frame of reference, of all the pixel of the blob, weighted by the corresponding pixel value of the given image: $$ G_w = \frac{\sum_{i=1}^N I(p_i) p_i}{\sum_{i=1}^N I(p_i)} $$ ### Size and Extent | Feature | Method | Data type | [Frame of reference](#easyobject-objects-features-frame) | |---------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------| | Area (pixel count) | [`GetArea`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ab7701cf7280c9d9c58c2b067d666c82f) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a807e9297872bc0f37f3d4c9d49f29e7f) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ab6c096859609e22b51074e2890e4d008) | `unsigned int` | pixel | | Bounding box limit

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(top, bottom, left, right) | [`GetTopLimit`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a5964e81a772abf2a96ee92152a88319b) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a591bbcfb46f789c026a7a3d2515e7761) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a585e1420acc785e61ca0da4be590f8fd)

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[`GetBottomLimit`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ad317287d36c2434c11b7bb4e2927b090) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#af6f925bf3339559c721907e58957c152) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ae648feaaa6b97230677df991f5917c7d)

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[`GetLeftLimit`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a695ef43de670db8e32895337cea44da4) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a3481601f3bf36a7c05462a404fb2c417) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a58bcb3e9b2b519ce2a6e6e8b972cab47)

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[`GetRightLimit`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a3768183f35cfc9b1a2a114bdb72b48e6) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a41fbf2240634a18d22a318b3bced427d) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ad686e144d5284b931574c6d19f333670) | `int` | pixel | | Feret box

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(center X and Y, height, width with distinct orientation angles at 22, 45, 68 degrees) | [`ComputeFeretBox`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a57b6255c10c96e0e6780ff4bb1bacbe6) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a372aadd42d0995ebff8f3c1ec710b791) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a286e90c5da56726d9841bcaae097bc84)

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[`GetFeretBox22Box`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ab1902e5e76383fa8182ba008bffb2b51) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ad180db4af74e9637b7d92af69f24c646) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ad4e94d7611c542da35e02c1c63845223)

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[`GetFeretBox22Center`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a0594f70c81e0e41f5d73aa24e4fc3ac2) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a6d9c4a1cc9a6af269ec3ae77c2b1f5f6) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a6491d12dd97da4971a40386826fd4d88)

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[`GetFeretBox22CenterX`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a2d1c02346356f60bbdf0f8215829407b) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a5a7ce7ecbef209e603f2e425569513e5) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ad32710924290bc7cddc8df26f59bb63e)

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[`GetFeretBox22CenterY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a82d0aaaba17457866a29c1f563196e9c) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#adfd665516d5b911bca9e45ca730dfc46) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a01345cd2ae46b2a8ab050e9d521ccf1e)

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[`GetFeretBox22Height`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a1a1c04e647814d933c690537a9e69cc3) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#aae9c8e2a61475fc9bbe0b591236171c9) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a759f1d5075061b4c8071172dea7399e2)

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[`GetFeretBox22Width`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a8b307f45ea2b30994d5d131f498da995) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ac205f09e2eedd73cd3dcf6f1d2a3d969) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a2d598f1993cf88ed64663eb372b55c41)

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[`GetFeretBox45Box`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a1f10ff3f31ea38691faf7f04e4698a21) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ab326bf720fa6c240d10e4bd8698fd648) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a204a8f64e5c89380eddace18cb2e225f)

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[`GetFeretBox45Center`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a990b530e97942b9160d5c5e8564059e7) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#aec0ba9b59aa3ae7b7a2a9a37db02c75e) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a4072eb6d4db2090bf2233bcf1fb95eda)

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[`GetFeretBox45CenterX`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#aa6b58153d4f64bf3dede77154f9e14da) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a616f63342877d6578137c11c4e9f8eba) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a7640a68e0462e2b0ac486799d1c6d95c)

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[`GetFeretBox45CenterY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a6b99b78d9c78217a119a45ac8612ee66) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a116cfb6e319e9419cf709e87b5840c75) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#af5d750eb8a299203b67173fbd5d46381)

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[`GetFeretBox45Height`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a5af8323461f50b8e98965fe12c620150) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#af1ddbe675e30f03af1e7f08158c392d3) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#adfdf2637568c22c1bf380ff0652e8b7a)

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[`GetFeretBox45Width`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a01c08d96a921592381168c96873a2e08) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a776533c995bb8caec0f3b603bf2e8449) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a288f38b648f47851b90546e871952007)

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[`GetFeretBox68Box`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a77a258be83870bef68c1281d02d6916d) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a3aa5135e327153e13fefbe7177168ecd) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a21904b3d9bb53a5ee2b0ca9a93e491c2)

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[`GetFeretBox68Center`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a45b5e55081b7ee36f600149cf3877a34) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a978ca71dce9e0d140b2716ceb91e73b7) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ad45a4341be5e564a3b302dd3a5d69931)

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[`GetFeretBox68CenterX`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#aaa6240e2becb8a9168b46ee947ea5c06) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ac761174e010747c044e127bd81838582) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a2444c222e6910d66e600836128b28771)

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[`GetFeretBox68CenterY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a488a032e1587ac5a6d86f4c75eb35121) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ab8e489b2443c3d579fbe1bd91abf597f) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a89b4c58838c9a2ac3ff66a479dd2be6c)

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[`GetFeretBox68Height`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a5516c54a617af82096f87e7d75abf189) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a14aa34f17c7e3d6304e20399a9b383a0) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a09e7c9756fc17b0076f2fe4811b50f6e)

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[`GetFeretBox68Width`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ab688e2ff4124150365636d8cc338ae0b) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a0b39a442c2dd31667656b05c829e895f) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#aee25e1ad304ca59a8da6e0e6ce199f3a) | [`ERotatedBoundingBox`](../../../doxygen_cpp/classeVision_1_1ERotatedBoundingBox.html) [_.NET](../../../doxygen_cs/classeVision_1_1ERotatedBoundingBox.html) [_Python](../../../doxygen_python/classeVision_1_1ERotatedBoundingBox.html)

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`float` | frame | | Min. enclosing rectangle

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(angle, center X and Y, height, width) | [`GetMinimumEnclosingRectangle`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a6d45ce303696897fb459d0591911afb2) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a046dd0b682a21a07960715df1604a006) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a8249526d64069f8533c9e7a18f5efa79)

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[`GetMinimumEnclosingRectangleAngle`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a57da64ed5bae440c8fd094cd0ae1da58) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a029424890afcd06bdc51f6fe1d9ed436) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a552d641b899c877bb2f99b28acdced81)

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[`GetMinimumEnclosingRectangleCenter`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a60bb832f2746f2cc3e8ebd04d1437810) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ade63060002d598886ddb33df921e0398) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a0ebf4cfe6196805f4b301bf0972eb666)

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[`GetMinimumEnclosingRectangleCenterX`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a135ecbe6ff1f688205300192398bb42b) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a317c021651aea1b867fd56a4c0e64f0d) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ab60bc1ad77cc26510387bbe40225eb30)

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[`GetMinimumEnclosingRectangleCenterY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#afc2d8cabd6270b731baba96b6f5ecac6) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a04c779241465d42e682e823e8240fc2b) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a457c92cc1b069c4106e281833f6c3aeb)

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[`GetMinimumEnclosingRectangleHeight`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a4ff53c782422ebf966136fb178da070b) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a5ea0f3ff97ec2e26b30ec8d778e7fbbb) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a8b31004a4bd9efb81a3adf675d71cfd6)

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[`GetMinimumEnclosingRectangleWidth`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#aa54ec611e733427331888634f44940c6) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a90ecea1f45432107ce1e69e1c0d3943e) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a20e6a39d47d63ee20c417798baf7f3ba) | [`ERotatedBoundingBox`](../../../doxygen_cpp/classeVision_1_1ERotatedBoundingBox.html) [_.NET](../../../doxygen_cs/classeVision_1_1ERotatedBoundingBox.html) [_Python](../../../doxygen_python/classeVision_1_1ERotatedBoundingBox.html)

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`float` | frame | A **Feret box** is a rectangle with the minimum surface rotated at a specified angle that contains all the pixels center points of an object. - **Bounding box** is the Feret box at 0°. - **Minimum enclosing rectangle** is the Feret box with the minimum surface across all the possible angles. - **Width** of a **Feret box rectangle** is the length of the rectangle side that exhibits the smallest angle with the X-axis. This is NOT necessarily the smallest side! - The **height** of a Feret box rectangle is the length of the other side of the rectangle. - Use [`ComputeFeretBox`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a57b6255c10c96e0e6780ff4bb1bacbe6) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a372aadd42d0995ebff8f3c1ec710b791) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a286e90c5da56726d9841bcaae097bc84) to compute a Feret box with an arbitrary angle. - The angle is measured clockwise from the X axis to the width side of the rectangle as shown in the image below:  ### Miscellaneous | Feature | Method | Data type | [Frame of reference](#easyobject-objects-features-frame) | |-------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------| | Starting point of the object contour

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(X and Y) | [`GetContour`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a8c536b68d3e767a1780a8e7e3cbb494e) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#af82d37fe472a5537a7a3e0d8c3872a9b) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#aaf8e5aaa1d174fd1e7f75aa64309e4fc)

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[`GetContourX`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a387010c296fc2b604451249f75cb4841) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a507494e1e30ccf09fdc9e48ad38e5de2) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a3a286a4e1bfb479875034bdc2c61aa4f)

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[`GetContourY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ad0e071c2c7615719c647c92ae2751599) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ab1a19b4911698ff5ddcb88069ce5c776) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#abe3527d2e5d156e053a3e675c6f3f0ba) | [`EPoint`](../../../doxygen_cpp/structeVision_1_1EPoint.html) [_.NET](../../../doxygen_cs/structeVision_1_1EPoint.html) [_Python](../../../doxygen_python/classeVision_1_1EPoint.html)

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`int` | pixel | | Path of the object contour | [`GetContourPath`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#abf69bb81c4dc214f6a1ee3c33a98eb80) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#abb7ae3f9b7b34df0f40731605b6de590) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a72ab93817187fcee96f59454b7a09036) | [`EPathVector`](../../../doxygen_cpp/classeVision_1_1EPathVector.html) [_.NET](../../../doxygen_cs/classeVision_1_1EPathVector.html) [_Python](../../../doxygen_python/classeVision_1_1EPathVector.html) | pixel | | Pixel gray-level value

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(min and max) | [`ComputePixelMax`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a89394e4898d070af0754d2c77eae122d) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a8b12f9f5a74e5740439eb687b3842cbb) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a09f5c440867e6d4c9c08e504a9c16c18)

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[`ComputePixelMin`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a8db00401dc0f8fd31a8a9f0d5e2820ba) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#af7f7445432f714281ffe16b59ab5773a) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a657d26057b1a27017ba46bbf336f1698) | [`EBW8`](../../../doxygen_cpp/structeVision_1_1EBW8.html) [_.NET](../../../doxygen_cs/structeVision_1_1EBW8.html) [_Python](../../../doxygen_python/classeVision_1_1EBW8.html) | n.a. | #### NOTE The object perimeter in pixels can be measured indirectly by tracing the object contour with contouring methods and counting the pixels. ### Moments and Ellipse of Inertia  | Feature | Method | Data type | [Frame of reference](#easyobject-objects-features-frame) | |--------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------|---------------------------------------------------------------------| | Eccentricity of the ellipse of inertia | [`GetEccentricity`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ad3c2c7243fee40b6a3eae4bc0d5d1258) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a892e032c4ee6e94de57fbe53ac6c3e4c) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a308f14fe10ab638e78159f13f1d8774d) | `float` | frame | | Moments | [`GetCentralMoment`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a6ed90230e7a30d87e43b930963982223) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#aa7282efda88a910eb349be7419c36316) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a0ee0dcf6a38702195ecd607f8159899e)

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[`GetMoment`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a04e3a404c44427098c8dfee65e18d8d9) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a34888bacbbdfa525e519a64a7390ee24) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ab3aad539475c8f4e83af5e27005a639b)

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[`GetNormalizedCentralMoment`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a5fb4ae99b281280f879b2426abd0f6f2) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a1516853b4590578beb54d89c3883d771) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ad34a059967ca678e32b1e692c01b101b) | `float` | frame | | Ellipse

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(angle, height, width) | [`GetEllipseAngle`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a56017d9ff7f410cc6162376f1d9f8f2d) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ae08b3ece5c1b171091e0964ea47b13d4) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#abebe3d23bf1c93ca1f56115e2206eb1c)

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[`GetEllipseHeight`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a07e2817a009bc3edef75a6c0da432d13) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a6db257ed4624e24075aec092805ac28c) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#aa9a42579ecdc9fce128c8bd998a3eb08)

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[`GetEllipseWidth`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ae154db2506e7637071b887ec0916a2ea) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a91d2f20ddb2b5a657288cb4366d4fb04) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ab9fa2a41c2e2a9fd6e38d485e1419190) | `float` | frame | | Centered moments of inertia

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(Sigma: X, XX, XY, Y, YY) | [`GetSigmaX`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a66e2f34bcdc561b08cd8711b3c19b972) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a69fd4fc624bbd0cde11561385f31b0c5) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a08cf7edf6892324bc4be197ba0c3e3a1)

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[`GetSigmaXX`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a6087a6502d0f8588e167dbb3fa377ecb) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a4a94c15d6d2ab258ad92958fc88312bc) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a78fa30501e0f5fc0d1c92de2a7063834)

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[`GetSigmaXY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a4d6e99ce8e7ea9eb449767873f077a3b) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#af6bca4634d8b1e4cbe4cb65e4f38f820) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ae368b7c366019cc7710305016dd89477)

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[`GetSigmaY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a1d3f15619caf80308ec349601a999ec6) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ac99c21cb11e989c154b4f1ef47811c97) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a6238fc9129cd38eba8384823a3150aa6)

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[`GetSigmaYY`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a985050f11f9e1e66548b84d271010804) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#ae53e4deb8c74b8edf2a1c8358f6ee292) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a40a960d7f1bc9b34962bc847460d289e) | `float` | frame | Given $N$ is the number of pixels of the blob, $x_i$ and $y_i$ the x and y coordinates of the $i$-th pixel of the blob, expressed in the frame of reference used to encode the image, the [`raw moment`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a04e3a404c44427098c8dfee65e18d8d9) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a34888bacbbdfa525e519a64a7390ee24) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ab3aad539475c8f4e83af5e27005a639b) of order $(p, q)$ is: $$ M_{pq} = \sum_{i=1}^N x_i^p y_i^q. $$ The [`central moment`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a6ed90230e7a30d87e43b930963982223) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#aa7282efda88a910eb349be7419c36316) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a0ee0dcf6a38702195ecd607f8159899e) of order $(p, q)$ is: $$ \mu_{pq} = \sum_{i=1}^N (x_i - \bar{x})^p (y_i - \bar{y})^q. $$ where $\bar{x}$ and $\bar{y}$ are the averages of all the $x_i$ and $y_i$. The [`normalized central moment`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#a5fb4ae99b281280f879b2426abd0f6f2) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a1516853b4590578beb54d89c3883d771) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#ad34a059967ca678e32b1e692c01b101b) of order $(p, q)$ is: $$ \eta_{pq} = \frac{\mu_{pq}}{\mu_{00}^{1+\frac{p+q}{2}}}. $$ The centered moments of inertia $\sigma_x$, $\sigma_y$, and $\sigma_{xy}$ are defined as: $$ \sigma_x = \frac{\mu_{02}}{N} = \frac{1}{N} \sum_{i=1}^N (y_i - \bar{y})^2 $$ $$ \sigma_y = \frac{\mu_{20}}{N} = \frac{1}{N} \sum_{i=1}^N (x_i - \bar{x})^2 $$ $$ \sigma_{xy} = \frac{\mu_{11}}{N} = \frac{1}{N} \sum_{i=1}^N (x_i - \bar{x}) (y_i - \bar{y}) $$ They can be grouped into the tensor of inertia: $$ \left( \begin{array}{cc} \sigma_x & \sigma_{xy} \\ \sigma_{xy} & \sigma_y \end{array}\right). $$ $\sigma_{xx}$ and $\sigma_{yy}$ are the largest and smallest eigenvalues of this matrix and are also called the first and second centered principal axis of inertia: $$ \sigma_{xx} = \frac{\sigma_x + \sigma_y}{2} + \frac{\sqrt{4\sigma_{xy}^2 + (\sigma_x - \sigma_y)^2}}{2} $$ $$ \sigma_{yy} = \frac{\sigma_x + \sigma_y}{2} - \frac{\sqrt{4\sigma_{xy}^2 + (\sigma_x - \sigma_y)^2}}{2}. $$ The width ($w$), height ($h$), and angle ($\theta$) of the ellipse of inertia are: $$ w = 4 \sqrt{\sigma_{xx}} $$ $$ h = 4 \sqrt{\sigma_{yy}} $$ $$ \theta = \frac{1}{2}\arctan\left( \frac{2 \sigma_{xy}}{\sigma_x - \sigma_y} \right). $$ The eccentricity, or object elongation, is: $$ \sqrt{1 - \frac{\sigma_{yy}}{\sigma_{xx}}}. $$ #### NOTE The moments of inertia $\sigma_x$, $\sigma_y$, and $\sigma_{xy}$ are also commonly noted as $I_x$, $I_y$, and $I_{xy}$. The moments of inertia around the X or Y axis are also the variance of the Y and X coordinates of the blobs respectively. ### Convex Hull The [`convex hull`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#ae0c61291f53047a6a8d7edbc449e9651) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#a94454ee1877dadde8758e07bf06d7d5e) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#aab3c03a55d3a9567051196eef0e0ee10) hull of a shape is the convex polygon of minimum area that completely surrounds an object. The convex hull can be used to characterize the object footprint, as well as to observe concavities. Given that the number of vertices of the convex hull is variable, they are stored in a [`EPathVector`](../../../doxygen_cpp/classeVision_1_1EPathVector.html) [_.NET](../../../doxygen_cs/classeVision_1_1EPathVector.html) [_Python](../../../doxygen_python/classeVision_1_1EPathVector.html) container. The convex hull is computed in pixel coordinates.  ## Graphic Representation The objects can be drawn onto the source image by means of [`ECodedImage2::Draw`](../../../doxygen_cpp/classeVision_1_1ECodedImage2.html#a5d7c466c4a883bb60de710d3fba8a018) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedImage2.html#afbd310e1a51562e3cf5f1c7801bdd049) [_Python](../../../doxygen_python/classeVision_1_1ECodedImage2.html#a0a9c71274421f2dd5b10cc0cf4980a18). The following features also have a graphical representation that can be drawn by the means of [`ECodedImage2::DrawFeature`](../../../doxygen_cpp/classeVision_1_1ECodedImage2.html#a34dc05727d86c6f245c626ac38547208) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedImage2.html#a8a0315bf562262a9242d2da02d06c77c) [_Python](../../../doxygen_python/classeVision_1_1ECodedImage2.html#a1840ecc38ea367b3568df40f2c8fb016). #### Drawable features and their default appearance. | Objects | Graphic | |--------------------------------|----------------------------------------------| | Bounding box |  | | Contour |  | | Convex hull |  | | Ellipse |  | | Feret box |  | | Feret box with an angle of 22° |  | | Feret box with an angle of 45° |  | | Feret box with an angle of 68° |  | | Gravity center |  | | Minimum enclosing rectangle |  | | Weighted gravity center |  | ## Runs For the sake of computational efficiency, the objects are described as lists of runs. A run is a sequence of adjacent pixels that share homogeneous properties (such as being above a given threshold). These runs are merged in objects by the image encoder.  **EasyObject** can work at object level, and at run level which allows faster processing in critical cases. This is useful to compute custom features on objects then list all runs belonging to a given object. Use [`ECodedElement::GetRunsIterator`](../../../doxygen_cpp/classeVision_1_1ECodedElement.html#abcd74e3a67216e9fd6185105142eafc3) [_.NET](../../../doxygen_cs/classeVision_1_1ECodedElement.html#aab4c60052747c42d74eb43c82be936ff) [_Python](../../../doxygen_python/classeVision_1_1ECodedElement.html#a588d46b3c4b6c7425a017e92a5452d5c) to get an [`EObjectRunsIterator`](../../../doxygen_cpp/classeVision_1_1EObjectRunsIterator.html) [_.NET](../../../doxygen_cs/classeVision_1_1EObjectRunsIterator.html) [_Python](../../../doxygen_python/classeVision_1_1EObjectRunsIterator.html) iterator object. #### SEE ALSO See the [code snippets](../../../resources/code_snippets/matching_and_measurement/easyobject/objectruniterator.html.md) showing how to loop over the runs of an object.